Pour equal parts of vegetable oil and olive oil into a large frying pan to reach a depth of 2 inches. Heat the oil over medium heat until a deep-fry thermometer registers 375 degrees F.
Roll out the dough on a lightly floured surface to 1/2-inch thickness. Using a floured 2-inch biscuit cutter, cut out doughnut rounds. Using a floured 1-inch biscuit cutter, cut out a hole in the center of each doughnut. Gather the dough scraps and re-roll to cut out more doughnuts.
Whisk the sugar and cinnamon in a medium bowl to blend. Set the cinnamon-sugar aside.
When the oil is hot, working in batches, fry the doughnuts until they puff but are still pale, about 45 seconds per side. Using a slotted spoon, transfer the doughnuts to paper towels to drain. Cool slightly. While the doughnuts are still warm, add to the bowl with cinnamon-sugar and generously coat each 2 times with the cinnamon-sugar. Serve warm.
Alternately, cool the fried doughnuts to room temperature. Stir 3 ounces milk chocolate and 1/4 cup whipping cream in a heavy small saucepan over medium-low heat until the chocolate melts. Set aside until the chocolate sauce comes to room temperature but does not set. Dip 1 side of each doughnut into the chocolate mixture. Sprinkle with finely chopped toasted almonds or crushed espresso beans and set aside until the chocolate is set.