Preheat the oven to 375°F (190°C) and lightly grease two standard donut pans with cooking spray. Swirl a paper towel inside each donut well to make sure the grease is evenly distributed and to dab off any excess.
Rinse and hull 4 large strawberries. Use a blender to puree them. (Four large strawberries should yield about 1/4 cup puree). Set aside.
Use a coffee grinder or food processor to grind 1/2 cup of freeze-dried strawberries into a fine powder. Whisk the strawberry powder with the flour, baking powder and salt in a medium mixing bowl.
In a large bowl, cream the butter, vegetable oil and sugar until smooth. Beat in the eggs one at a time, scraping down the sides of the bowl to ensure each egg is incorporated completely into the batter. Mix in the vanilla.
Stir in 1/3 of the flour mixture on low speed, followed by the puree, another 1/3 of flour, the milk and the remaining flour. Stir until just combined. The batter will be thick and a little sticky.
Scoop the batter into a ziplock bag or large piping bag and cut off the tip so that you have an inch-wide opening. Pipe the batter evenly among the 12 donut wells. Smooth out the tops with a spoon or leave as is. This will be the bottom of your donuts.
Bake for 7-9 minutes, or until a toothpick inserted in a center donut comes out clean. Leave the donuts in the pans for 3 minutes before transferring them to a wire cooling rack. Use a knife to gently remove the donuts from the pans. The tops will be lightly browned.