Preheat oven to 375 F. Spray 9x13-inchbaking dishwith nonstick cooking spray.
Bring water to a boil and cooklarge shells according to package directions. When the shells have two minutes left to cook, add in the broccoli. Strain the pasta and broccoli together.
While the water is boiling for the pasta, melt the butter and saute the ham, garlic, thyme, salt, and pepper for a few minutes.
Once the butter is melted, stir in 2 cups of shredded cheddar and whipping cream. Stir until the cheese is melted and the mixture is bubbly and thick.
Pour the pasta and broccoli into the prepared baking dish. Top with the ham mixture. Stir gently and sprinkle with the 1/2 cup of shredded cheddar. Bakein the preheated ovenfor about 15 minutes until mixture is bubbly.
Remove from the oven and serve hot as one dish dinner, or with side salad.