Preheat the oven to 375 degrees F (190 degrees C). Line a 6-muffin tin with paper muffin cups.
In a medium-sized bowl, add warm water, yeast, and sugar. Stir, then let sit for 5 minutes, or until fully bloomed.
To the yeast mixture, add flour, olive oil, salt, Cheddar cheese, and Parmesan cheese. Mix to form a shaggy dough.
Turn dough out onto a clean work surface, Knead dough for 4 to 5 minutes or until all ingredients are incorporated and dough is a smooth, shiny ball.
Place dough back in the bowl, cover with plastic wrap and let rest until doubled in size, about 1 hour.
Punch dough down, then break into 6 even parts. Roll each part into a soft ball, then place each ball into the prepared muffin tin.
In a small bowl, add butter, rosemary, and garlic. Mash with a spoon until combined. Spread some of the mixture gently on top of each muffin.
Bake muffins in the preheated oven for 15 minutes, then check for color. Bake until golden brown, about 5 minutes more. Serve warm.