In a medium saucepan, set over medium-low heat, warm the milk to 100F to 110F and pour into the mixing bowl of a stand-up mixer with the hook attachment on. Add the dry active yeast and allow it to stand until mostly foamy, about 10 minutes. Add the melted butter, vegetable oil, egg, flour, sugar and salt.
Turn the mixer to medium-low and mix until totally combined.
Turn the mixer to medium/high and knead the dough is smooth and sort of pulls away from the sides of the mixing bowl, 7 to 10 minutes. The dough will be slightly sticky. Grease a medium, clean bowl with cooking spray or olive oil. Form the dough into a ball (some will stick to your hands, don't worry) and place in the bowl and cover with plastic wrap. Transfer to the fridge to rise for 1 hour or overnight.
Line a baking sheet with parchment. Dust a work surface and the top of the dough in the bowl with a little bit of flour. Punch down the dough and transfer it directly to the floured surface. Roll it out, using a rolling pin, to a 1/2-inch thickness.
Use a 3-inch round cutter and 1 1/4-inch round cutter to cut out your doughnuts. Cut out as many as you can and re-roll the scraps and cut out a few more. You should end up with about 12.
Transfer the doughnuts to the parchment lined baking sheet, spacing them about 2 to 3 inches apart. Spray the tops with a bit of cooking spray and lightly cover with plastic wrap. Allow to rise for 45 minutes, until almost quartered in size.