Preheat oven to 350ºF. Grease a 6-cup muffin tin.
Measure the flour, baking powder, salt, and baking soda into a large bowl. Stir together with a fork until blended.
Add the cheese, and stir the blend.
In a second bowl, add the lemon juice, yogurt, olive oil, and egg. Blend together to combine.
Make a well in the middle of the dry ingredients, and pour in the yogurt mixture. Stir by folding over only until just combined.
Add the basil, chili powder, and lemon zest last, folding them in only once or twice to distributed evenly.
Divide between the six muffin cups.
Bake for 15 to 20 minutes, or until a knife tip or toothpick emerges clean.
Let the muffins cool for about 10 minutes before removing them from the tin, and transferring to a wire rack.