Cake doughnuts are easy to make and form a perfect soft base for ice cream sandwiches. Adding juicy blueberries to the batter before baking adds a summery burst of flavor. Be sure to toss the blueberries in a little bit of flour—this helps keep them suspended in the batter rather than sinking during baking.
Place an oven rack in the center of the oven and preheat to 425 degrees F. Lightly spray a 6-cavity doughnut pan with nonstick spray and place on a baking sheet.
In a small bowl, toss the berries with 1/4 cup of the flour. Set aside.
Whisk the remaining 1 1/4 cups flour, baking powder, salt and cinnamon together in a medium bowl. In another medium bowl, use a spatula to stir the oil and butter together, then add the granulated sugar, brown sugar and lemon zest and mix well to combine. Switch to a whisk and whisk in the egg, whisking well to combine. Whisk in the vanilla.
Add half of the flour to the butter mixture and stir with the spatula to combine. Add the buttermilk and mix to combine, then mix in the remaining dry ingredients just until smooth.
Transfer the batter to a disposable pastry bag or resealable plastic bag, then cut a 1/2-inch opening from the tip (or the corner of the bag). Pipe the batter evenly into the cavities of the prepared pan, filling each about three-quarters full.
Press about 8 floured blueberries into each doughnut, pressing to nearly submerge them in the batter. Bake until the doughnuts are puffed and spring back when pressed gently, 7 to 9 minutes. Invert the pan over a cooling rack to release the doughnuts. Cool completely.
Slice each doughnut in half horizontally with a serrated knife. Scoop softened ice cream onto the bottom half of each and cover with the tops. Freeze for at least 15 minutes before serving. The sandwiches can be frozen in an airtight container for up to 2 weeks.