Preheat oven to 350°F. Lightly grease an 8 ½-by-4 ½-inch loaf pan; line with parchment paper, leaving a 2-inch overhang on long sides.
Whisk together flour, baking powder, salt, and pepper in a bowl. Add feta and spinach; toss to coat. Whisk together oil, buttermilk, and eggs in a second bowl. Add wet ingredients to dry ingredients and stir until combined. Transfer batter to prepared pan.
Bake until a toothpick inserted into center comes out clean, 55 to 60 minutes. Cool in pan on a wire rack 10 minutes, then use overhangs to remove from pan and transfer to rack; cool completely.
