In a medium mixing bowl, combine 1 cup of plain yogurt, 3/4 cup of granulated sugar, and 3 large eggs. Use a whisk to beat the ingredients together until the mixture is smooth and well-combined, about 2-3 minutes.

Sift 1 1/2 cups of all-purpose flour, 1 1/2 teaspoons of baking powder, and a pinch of salt into the yogurt mixture. Gently fold the dry ingredients into the wet ingredients using a rubber spatula.

While folding in the dry ingredients, preheat your oven to 350°F (175°C).

Carefully pour the batter into a greased 9-inch round cake pan, spreading it evenly. Tap the pan gently on the counter to release any air bubbles that may have formed.

Place the cake pan in the preheated oven and bake for 25-35 minutes. Keep an eye on the cake; it's ready when the top is golden-brown and a toothpick inserted comes out clean.

Once baked, remove the cake from the oven and allow it to cool in the pan for about 10 minutes. Then invert it onto a wire rack to cool completely.