In a small bowl, mix together water, yogurt, 1/4 c. oil and egg yolk. In the workbowl of a food processor, pulse together flour, sugar and yeast to combine. With the motor running, slowly add the liquid ingredients to the flour. Process until combined. Let mixture rest for 10 minutes.
Add salt and process another 30-60 seconds. It will form a sticky dough that should clear the sides of the food processor workbowl.
Scrape dough out onto a floured worksurface and knead just until smooth, about a minute. Form into a ball and place in a lightly oiled bowl (large). Cover tightly with plastic wrap and refrigerate 16-24 hours.
After the dough has rested, turn out onto a lightly floured work surface and divide dough into 4 pieces and shape each piece into a ball. Cover lightly with plastic wrap and let rest 15-20 minutes.
Meanwhile melt the butter in a small saucepan, then add the garlic. Set aside.
Roll the first piece of dough out into a 9 inch round. Using a fork, poke the dough all over, 20-25 times. Lightly mist the top side with water.
Heat the remaining oil in a large nonstick skillet over medium heat until the oil begins to shimmer. Wipe the oil out of the skillet with paper towels, then add the rolled out dough, sprayed side down and spray the other side lightly. Cover skillet and cook until spotty brown underneath, 2-4 minutes (poke any large bubbles that form). Flip naan, cook, covered, another 2-3 minutes until browned. Flip again, brush with butter, then transfer to a plate and cover with foil. While rolling out and cooking the remaining naan.