In a large mixing bowl, beat together butter, sugar, and extracts until creamed and evenly combined. Beat in the egg, until evenly combined. Now the sour cream, again until evenly combined.
In a separate, large mixing bowl, add the flour, baking powder, and salt.
With the mixer on low speed, slowly add the flour mixture, a little at a time, and mix in until evenly combined- the dough will be slightly sticky. Wrap and seal the dough in plastic wrap. Refrigerate for 30 minutes.
Lightly flour a flat work surface. Roll the dough out and knead it 3-4 times. Roll the dough out to 1/2 inch thickness. Use a donut cutter to cut donuts. Re-rolling the scraps as necessary.
Fill a dutch oven halfway with oil, and heat over medium heat until a thermometer registers 350 degrees. Cook the donuts in batches of 4-5, about 1 1/2 minutes per side, Remove the cooked donuts to paper towels, to drain completely. Let the donuts cool to room temperature.