Heat olive oil in a skillet over medium heat. Stir in garlic and cook until fragrant, about 1 minute. Add dandelion leaves and season with salt and pepper. Cover and cook until dandelion is wilted, stirring occasionally, 3 to 4 minutes. Stir in mozzarella cheese and Parmesan cheese until melted. Remove from heat and set aside.
Combine water, honey, and yeast in a large bowl. Allow yeast to proof until a creamy foam forms on top. Add flour and salt. Knead mixture until a dough forms, adding flour as needed if dough seems too wet.
Roll out dough on a lightly floured surface with a lightly floured rolling pin until it is about 1/4-inch thick. Spoon dandelion mixture on top. Roll dough starting from one side into a log shape; make slits on top using a sharp knife. Cover with a damp towel and set in a warm location to rise, about 20 minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Combine garlic and melted butter in a small bowl and brush mixture on top of the loaf.
Bake in the preheated oven until golden brown and a toothpick inserted into the center comes out clean, about 25 minutes.
