Special equipment: a 7-by-3-inch round cake pan
For the cake: Preheat the oven to 350 degrees F. Butter a 7-by-3-inch round cake pan.
Whisk together the sugar, oats, baking powder, salt, baking soda and 1 1/2 cups flour in a large bowl and set aside. Toss the blueberries with the remaining 1 tablespoon flour in a small bowl.
Whisk together the oil, yogurt, vanilla and eggs in a medium bowl. Fold the oil mixture into the sugar mixture until just combined. Then gently fold in the floured blueberries.
Pour the batter into the prepared cake pan and bake until a toothpick inserted in the center comes out clean, 55 minutes to 1 hour 5 minutes.
Cool in the pan on a rack for 30 minutes. Unmold the cake and cool completely on the rack, about 30 minutes more.
For the frosting: Meanwhile, beat the yogurt and cream cheese in a large bowl with an electric mixer on medium-high speed until smooth. Beat in the vanilla. Then slowly add the sugar, while beating, until completely combined. Refrigerate until ready to use.
Slice the cooled cake in half horizontally to make 2 rounds.
Put 1 cake round on a cake stand or round serving platter. Evenly spread half the frosting over the top of the cake, spreading all the way to the edge. Dollop half the blueberry preserves in several small drops all over the frosting layer. Top with the remaining cake round and spread the remaining frosting over the top. The sides of the cake will be unfrosted. Dollop the remaining blueberry preserves in the center of the cake. Sprinkle blueberries on top of the preserves. The cake can be served right away or made the night before and refrigerated.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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