Slice and stack the potatoes in a bowl. Cover with water while preparing the sauce, so the potatoes don't brown.
In a saucepan, melt the butter and sauté the onion and garlic for several minutes, until the onion is translucent.
Add the flour to the onion mixture and stir until the butter soaks up the flour. Add the broth, milk, thyme, and rosemary. Stir until mixture boils and thickens.
Spread a thin layer of sauce on the bottom of a greased 9x13-inch baking dish. Drain water from the potatoes and layer the potato slices over the thin layer of sauce.
Spread the remaining sauce over the top of the potatoes. Combine both cheeses and sprinkle over the top.
Bake at 425 degrees Fahrenheit for 30 minutes or until the potatoes are tender and the cheese bubbles and browns. *Optional: Sprinkle with fresh, chopped parsley for added color.
Notes
If dicing the potatoes, check doneness with a fork after 30 minutes. Then cover with foil and continue baking if necessary, until potatoes are done.