Mix warm water, sugar, and yeast; let sit 5 minutes until foamy.
Add flour, salt, and olive oil; knead 8 minutes until smooth and elastic.
Place dough in greased bowl, cover, and rise 1 hour until doubled.
Roll dough into 12x16 rectangle, spread garlic butter, and sprinkle cheeses.
Roll tightly, seal seam, cut into 8–10 pieces, place in baking dish.
Rest 20 minutes while oven preheats to 375°F.
Brush tops with butter and bake 25–30 minutes until golden and 190°F inside.
Brush again with butter, sprinkle parsley, and rest 5 minutes before serving.