1 cup whole or 2% plain Greek yogurt
2/3 cup olive oil, plus more for coating the pan
2/3 cup honey
1 tablespoon finely chopped fresh thyme leaves
1 teaspoon finely grated lemon zest
3 large eggs
1 1/2 cups all-purpose flour
1/2 teaspoon baking powder
1/2 teaspoon baking soda
1/4 teaspoon salt
Arrange a rack in the middle of the oven and heat to 325°F.
Grease a 9-inch round cake pan or springform pan lightly with oil. Line the bottom with parchment paper and grease the paper if using a cake pan.
Whisk together the yogurt, olive oil, honey, thyme, and lemon zest in a large bowl. Add the eggs, one at a time, whisking well after each addition. Add the flour, baking powder, baking soda, and salt. Stir with a rubber spatula until the batter is almost smooth with just a few small lumps, but do not overmix.
Transfer the batter to the cake pan, and use a spatula to spread it out evenly. Bake until the top is lightly browned and a tester comes out clean, 40 to 45 minutes.
Transfer the cake to a cooling rack and let it cool for 10 minutes before removing it from the pan. Run a knife around the pan to loosen. If using a springform pan, unclasp the sides. Otherwise, flip the cake onto a plate and flip it back onto the rack or serving plate. Serve warm or at room temperature.