There isn't a way to keep doing everything the same way you listed, and not have the puddle. But if you are willing to make some changes to your cooking process, you can get to cook without the puddle.
The important thing to understand here is that, if you are frying in a strict sense*, the fat is key. If you aren't (and with one or two spoons of fat, you aren't), you are very flexible in how you use it, or even whether you use it at all.
- Don't use any oil. As this is roasting, there is no actual need for any fat. The roasting will happen anyway, through the heat transfer from pan to food, and because the pan is nonstick, the food won't stick to the pan.
- Use much more oil. On a nonstick pan, the oil is not needed to prevent sticking, but it has another role: it prevents empty areas of the pan from overheating. If your food doesn't cover the pan surface, for example if you are making a steak, you should use enough oil to get a single pan-sized puddle, 1-2 mm deep, to not burn your PTFE.
- Don't use nonstick pans. You can make your roasted food in pans of other types too, like cast iron or enameled steel. The oil won't puddle on these surfaces.
- Coat your food The above methods assume that you are using the oil for its physical properties, to protect your pan. If you want the taste and texture provided by a thin coat of oil, you shouldn't be coating the pan in oil, you should coat the food. For steaks and other types of single-piece food, use a brush. For food cut into chunks, put it in a large bowl (2-3 times the volume of the food), pour the oil on top, and toss. This method is not suitable for liquid food (e.g. crêpes).
And at last, as dbmag9 suggested, you can just do nothing and live with the puddle. This will turn out to be equivalent to one of the above methods, depending on the food you are making.
Update If you were using a nonstick springform pan for baking, you would also have the option of using a lecithin spray. FuzzyChef pointed out in comments that this will ruin the pan if used on stovetop. So I removed the option from the list above.
* Explanation of what I mean by "frying in the strict sense".
The common use of the word "frying" nowadays covers several processes with different physics and usually rather different results in taste.
First, you have your deep frying. This involves your food floating in a very large bath of liquid fat, not touching the bottom of the pan.
Second, there is shallow frying. In this case, you carefully position chunky food on in the pan, filled up with oil to the middle of the chunks, so that the heat transfer is still coming mostly from the oil, and no juices can accumulate.
Third, there is stir frying in a wok. Here, you have very small pieces of food floating in the central puddle of super hot oil, they spend in it very short time, just to get a crust, and then get pushed up onto the hot walls to have some time in which the interior gets cooked through.
The fourth option is to use a minimally thin layer of oil between the pan and the food, and plop a few single pieces of food onto the pan or griddle - this can be a steak, or an egg, or American pancakes. The heat transfer happens almost directly from the pan to the food, since there is too little fat "to get in the way". I don't know an exact term for this preparation, and when I tried using "stovetop roasting" descriptively in the older version of this answer, people protested. Anyway, it produces a minimal crust that is more comparable to oven-roasted or to grilled food than the two other types of frying.
The fifth thing you can do is to use very small amounts of oil, and crowd your pan with a large volume of small pieces of food. Soon, the food exudes its own juices, which don't evaporate instantly, the way they would do in a fat bath, but pool around, and become the actual medium in which the food sits. This is technically equivalent to braising, even though many people nowadays don't use the word when they do this kind of dish.
(There probably are more techniques about which one can argue how they relate to the above ones, but these are the widespread ones which are relevant to thinking about the problem in this question.)
As noted in comments, all these five are covered by the same word, "frying", in current usage. I would consider the first three types to be "frying in the strict sense". They were historically the widespread ones. Anyway, each of the five works differently, and is a separate skill that a cook needs to learn to do well, so it makes sense to think about them separately and keep in mind which one is meant, even if the word used for them is the same.
