Bring a large pot of water to boil and add a dash of salt. Cut the potatoes into roughly 1-inch cubes. Place the potatoes into the boiling water for 10 to 15 minutes. Drain the potatoes and then return them to the same pan.
Place the butter, garlic and the thyme in with the potatoes and heat over a low flame until the garlic is just beginning to brown. Discard sprigs of thyme.
Remove the potatoes from the heat and pour in the cream, salt, pepper, pecorino-Romano cheese and blue cheese. Use the back of a fork or a masher to lightly mash the ingredients together, leaving some lumps in the potatoes if desired.
Place the potatoes into the bottom of a lightly greased 3-quart casserole dish.
In a small bowl, combine the olive oil, breadcrumbs, Parmesan cheese, rosemary and parsley. Spoon this mixture over the potatoes and bake the casserole, uncovered, in the oven for 20 minutes.