Place a rack in middle of oven; preheat to 400°. Brush a 9"-diameter cake pan with olive oil. Line bottom of pan with a parchment paper round; brush parchment with more oil. Whisk 1⅓ cups (208 g) yellow cornmeal, ½ cup (63 g) all-purpose flour, 2 Tbsp. sugar, 2 tsp. baking powder, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 1 tsp. freshly ground black pepper in a medium bowl. Whisk 2 large eggs, 1½ cups sour cream, ¼ cup olive oil, and ¼ cup water in a large bowl until homogeneous. Add dry ingredients; mix until almost combined. Add 4 oz. feta, crumbled, and gently fold to incorporate. Scrape batter into prepared pan.
Toss 8 oz. mixed heirloom cherry tomatoes, halved, and remaining 1 Tbsp. olive oil in a medium bowl. Arrange, cut side up, on top of batter; sprinkle with flaky sea salt. Bake cornbread until a tester inserted into the center comes out clean, 35–40 minutes. Transfer to a wire rack and let cool. Invert onto a large plate. Peel away parchment paper and turn right side up. Do ahead: Cornbread can be baked 2 days ahead. Wrap tightly and chill.
