Toss cheeses together in a medium bowl and put a small handful of cheese aside for sprinkling later. In a medium pot, melt 3 tablespoons of the butter over medium heat. Add onion and sauté until softened; add garlic and sauté another minute. Lower heat a bit, whisk in flour, and continue whisking 3 minutes to form a roux. Slowly pour in the hot milk, whisking constantly. Turn heat back to medium and cook until thickened, about 5 minutes. Remove from heat and whisk in Dijon, pepper, and thyme, then mix in the cheese and ham. Cover with lid and set aside.
Preheat oven to 375 F. Bake one can of crescent rolls according to package directions. Meanwhile, grease a 9-inch oven-safe skillet (cast iron preferred) with cooking spray. Roll the remaining can of crescent rolls and place them along the outer edge of the skillet, then spoon cheese mixture into the middle. Brush the crescents with a tablespoon of melted butter, then sprinkle with reserved cheese. Bake 15 to 17 minutes, until crescents are golden brown. Let cool a few minutes before serving fondue-style straight out of the skillet, tearing off pieces of crescent roll and dipping into cheese.
*For a smooth melted dip, freshly shred the cheeses rather than using pre-shredded.
