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 cookie cutter, cut out doughnut rounds. Using a floured 1-inch cookie 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.
Recipe courtesy Giada De Laurentiis