Preheat oven to 350 degrees F (175 degrees C). In a mixing bowl, whisk 1 cup sugar, flour, baking powder, and baking soda together until evenly combined.

Melt butter in a skillet over medium heat. Cook and stir the pitted cherries in the butter until they are tender, sprinkling them with 1 tablespoon of sugar, 8 to 10 minutes. Set aside.

Form a well in the center of the dry ingredients, and pour in 1/2 cup olive oil, eggs, and yogurt; use your fingers to lightly stir the liquid ingredients into the flour mixture to make a soft dough. Scrape the batter into a 9x12-inch baking dish. Drizzle the batter with 1 tablespoon of olive oil, and top with the cherries.

Bake in the preheated oven until the cake is set and golden on top, about 40 minutes. A toothpick inserted into the center of the cake should come out clean.