Mix the dough. Combine all dough ingredients in a bowl or bread machine bucket and mix until well combined. There is no need to proof the yeast first; simply combine everything. After a few minutes of mixing, evaluate the consistency of the dough and add more flour or water, a tablespoon at a time, if needed.
Knead. Knead the dough by hand, stand mixer, or bread machine for 8-10 minutes until it is smooth, elastic, and stretchy.
First rise. Cover the dough and let it rise in a warm place for 60 minutes until doubled in bulk. If your kitchen is cool, briefly turn on your oven, then turn it off to create a warm rising environment.
Divide and shape. Turn the dough out of the bowl or bread machine and divide it into 24 equal pieces. Shape each piece into a round roll by pinching the bottom to smooth out the top. Arrange in a 13x9 pan in a grid of 4 x 6 or around two round pie plates.
Second rise. Cover with greased plastic wrap and allow to rise until puffy, about 45 minutes. Preheat the oven to 375°F with the rack in the center toward the end of the rising time.
Make the topping. Combine melted butter, grated parmesan, and crushed garlic clove. Gently brush the mixture on top of the rolls.
Bake. Bake until golden brown (about 16-19 minutes for pie plates and 25 for 13 x 9). Remove and place the whole dish on a cooling rack. Serve directly from the pan or transfer to a serving dish.