Whisk together flour, baking powder and salt. Using a wooden spoon, stir in yogurt and 1/4 cup goat cheese. Knead on floured surface until smooth and elastic, about 10 minutes. Form into ball. Return to bowl; cover with plastic. Let rest 2 hours (dough will not rise).

Heat vegetable oil in a large pan over medium-high heat. Divide dough into 4 even pieces. Using the palm of your hand, press each piece into a flat, round disk, 6-8 inches in diameter. Gently transfer the naan to the hot pan. Cook until golden brown and crisp, about 2 minutes on each side. (The naan will bubble slightly and cook more in some spots than in others. I find that it sometimes even becomes nearly blackened in small spots, but this is part of what gives it that familiar “grilled” naan flavor.”) Serve immediately.