Directions

1. Melt 1 tablespoon butter in a large stockpot or Dutch oven over medium heat. Add ham, and cook, stirring occasionally, until lightly browned, about 3-4 minutes; set aside.
2. Melt remaining 3 tablespoons butter. Add garlic and onion, and cook, stirring occasionally, until translucent, about 3-4 minutes.
3. Whisk in flour and thyme until lightly browned, about 1 minute. Stir in chicken broth, scraping any browned bits from the bottom of the pot.
4. Stir in potato. Bring to a boil; cover, reduce heat and simmer, stirring occasionally, until potato is tender, about 10-15 minutes.
5. Using a potato masher, mash potatoes until desired consistency is reached. Stir in ham, broccoli and heavy cream. Cover and simmer until broccoli is tender, about 5-6 minutes.
6. Remove from heat. Gradually stir in cheese until smooth; season with salt and pepper, to taste.
7. Serve immediately.