Is there a way to make delicious donuts with a small amount of oil?
Donuts are a deep fried food. The texture of deep fried food is unique and cannot be duplicated by other methods. If you bake doughnut dough, you will get small rolls, which will have a similar aroma, but not the same combination of moist, soft inside and fat-crispy outside. You could bake it, as with any other yeast dough, only nobody will recognize it as a donut. 

Assuming that you want to get actual donuts, you must fry them. And no matter what you do to them, the more oil you use to fry them, the better your donuts will turn out. The physics of deep frying include throwing pieces of food with a starchy surface (potatoes, or breaded items, or dough pieces like donuts) in oil at around 190 degrees Celsius. At this temperature, the outer surface of the dough/vegetable/breading crisps immediately, preventing from any oil getting into the item and any vapor getting out of the item. 

This only works when the oil in the vicinity of the fried item stays within a few degrees of the target temperature during the first ~30 seconds of the frying process. Which means that you need a stable temperature in your fryer. Now, thermodynamics tells us that, if you throw a 25 degrees piece of food into a puddle of 190 degrees hot oil, they will exchange warmth proportionally to their mass. So, if you want the oil to stay close to the correct temperature, the mass of the donut has to be very small in comparison to the mass of the oil&nbsp;— which means that you need lots of oil. 

The options you have to do with less oil are all unsatisfactory from my point of view, you might decide to pick one of them. 


Put up with the quality reduction. Use less oil in the pan, maybe even shallow frying in oil up to the half of the donut only. The donuts will lose moisture and soak up grease. The less oil you use, the worse the grease soak will be. Also, you will use up more oil, because you will have to constantly add the amount soaked up by the already fried donuts. You may consider it well used instead of wasted, because you get to eat it, but from my point of view this is the worst option. 
Trade time for oil. You can use a small pot, and fry a single donut at a time. Frying 50&nbsp;g donuts should go well with under 500&nbsp;ml oil. You are still a bit constrained by the fact that the oil temperature will fluctuate more due to factors not related to the oil, but it should be manageable, if you have the patience. Note that if you place multiple donuts in the small pan, you are getting towards the first or third solution. 
Try to manage a stable temperature in a donut-crowded small pan by using a very hot setting and letting the oil get too hot before adding a new donut. This is a very complicated thing to manage, especially seeing that you are trying to not burn the other donuts in the pan at the same time. I don't think I could manage it, and if I could, the oil wouldn't be worth the stress. There is also the extra energy to consider&nbsp;— not as expensive as throwing out more oil, but probably worse from an environmental point of view. 


In the end, if you want good donuts, you have to use a pot/fryer where they can swim freely in oil. Any change you make to this setup reduces the quality of your donut, making it less donut-like.