In the bowl of a stand mixer, combine the warm water, active dry yeast, and 1 tablespoon of sugar. Stir briefly and allow the mixture to rest for 10 minutes, or until a frothy layer appears on the surface, indicating that the yeast is active.

Add the remaining ¼ cup of sugar, warm milk, beaten egg, and salt to the activated yeast mixture. Begin adding the bread flour gradually, starting with 3½ cups. Using the dough hook attachment, mix on medium-low speed until a soft dough forms. If necessary, add up to ½ cup more flour until the dough is pliable and slightly tacky but not sticky. Continue kneading with the mixer for 8–10 minutes until the dough is smooth and elastic.

Transfer the dough to a lightly oiled bowl, turning it once to coat all sides. Cover the bowl with a clean kitchen towel or plastic wrap and place in a warm, draft-free location. Allow the dough to rise for approximately 1 hour, or until doubled in size.

Once risen, gently punch down the dough to release air. Knead in the minced garlic until evenly distributed. Divide the dough into portions roughly the size of golf balls. Roll each piece into a ball and place them on a lightly greased or parchment-lined baking sheet. Cover loosely with a towel and let rise for another 30 minutes.

Preheat a grill to high heat and lightly oil the grates. Working one piece at a time, roll each dough ball into a thin circle on a lightly floured surface. Place the rolled dough onto the hot grill and cook for 2–3 minutes, or until the underside is puffed and golden with char marks.

While the first side is cooking, brush the uncooked top side with melted butter. Flip the naan, then brush the now-cooked side as well. Grill for an additional 2–4 minutes until the second side is fully cooked and golden. Repeat with the remaining dough. Serve warm for best texture and flavor.