Preheat the oven to 350°F. Line a round or square cake pan with parchment paper. If making individual cakes, line a muffin tin or grease well.
Prepare the citrus. Slice the fruit thinly. If you want to reduce bitterness, either peel the citrus completely or simmer the slices briefly in water with a little sugar, then drain and cool before using.
In a small bowl, stir together the melted butter and ½ cup sugar. Pour the mixture into the prepared pan and spread evenly. Arrange the citrus slices in a single layer over the butter-sugar mixture. Set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the room-temperature butter and sugar until light and fluffy, about 3–4 minutes.
Add the vanilla, citrus zest, and citrus juice. Mix until combined.
Add the eggs, one at a time, mixing just until incorporated.
With the mixer on low, alternate adding the dry ingredients and the buttermilk or yogurt, starting and ending with the dry ingredients. Add the dry ingredients in three additions and the wet in two, mixing just until combined each time. Do not overmix.
Spoon the batter gently over the citrus layer and smooth the top.
Bake for 35–40 minutes, until the cake is set and a toothpick inserted into the center comes out clean.
Let the cake rest in the pan for 10–15 minutes, then carefully invert onto a serving plate. Peel away the parchment.
Serve warm or at room temperature, with whipped cream or crème fraîche if you like.
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