In a large mixing bowl or the bowl of a stand mixer, whisk together sourdough starter and milk until well combined.
Add the flour, yogurt, olive oil, and salt to the sourdough mixture.
If using a stand mixer, use the dough hook set to low and mix the dough for about 5 minutes. If kneading by hand, mix the dough until it forms a shaggy ball. Turn the dough out onto a floured surface and knead for 8-10 minutes. The dough should be smooth, elastic, and slightly tacky.
Bulk ferment. Transfer the dough to a well-greased bowl, cover it with plastic or a damp dishcloth, and place it in a warm location to rise for 3-6 hours (this depends on how active your starter is and how warm the environment is).
When the dough has nearly doubled in size, punch it down and transfer to a lightly floured surface. Divide the dough into eight equal pieces, roll into uniform balls, and cover with a damp dish towel.
Rest. Set the dough aside to rest for 30 minutes (the dough isn't expected to rise again).
Preheat a cast-iron skillet to medium heat.
On a well-floured cutting board or counter, roll each dough ball to a thickness of slightly less than ¼ inch.
Lightly coat your preheated cast-iron skillet with olive oil. Cook each naan for 1-2 minutes per side. Flip the dough when the top begins to bubble.
Place the cooked naan aside to cool and brush with roasted garlic butter (instructions below). Repeat this process until all of your dough is cooked and buttered.