Preheat the oven to 350 degrees F. Spray an 8-inch springform pan with nonstick cooking spray.
For the crumble: Combine the melted butter, granulated sugar, brown sugar, salt and cinnamon in a medium bowl and stir until smooth. Stir in the flour and rolled oats, working the mixture to a crumbly texture. Set aside.
For the cake: Melt the butter and pour into a liquid measuring cup. Set aside.
Put the flour, granulated sugar, brown sugar, baking powder and salt in a medium bowl. Whisk to combine, breaking up any lumps of sugar. Set aside.
Add the vanilla, citrus zest, yogurt, egg and oil to the measuring cup of butter. Mix with a whisk or a fork to break up the egg.
Make a well in the center of the dry ingredients and pour in the liquid ingredients. Stir with a rubber spatula until the flour is almost incorporated. Gently fold about half of the raspberries into the batter.
Transfer the batter to the prepared springform pan and spread to smooth the top. Arrange the remaining berries on top of the batter and then sprinkle the crumble on top.
Place the springform pan on a rimmed baking sheet to prevent overbrowning the bottom of the cake. Bake until a toothpick inserted in the center comes out clean, 55 minutes to 1 hour. Let cool completely on a wire rack before serving.