Melt your butter in a saucepan over medium heat. Add the diced onion and minced garlic, cooking until soft, about 3 to 4 minutes.

Add your broccoli florets, chicken broth, and dried thyme into the saucepan. Cover and simmer for about 6 minutes, or until the broccoli turns tender.

Add your cream cheese into the pot and simmer for another 2 minutes, stirring until it melts into the broth.

Remove about a cup of the vegetables from the pot and chop them coarsely. Set this aside.

Using a hand blender, blend the remaining soup directly in the pot until smooth.

Pour your heavy cream into the blended soup and bring everything to a gentle boil.

Reduce the heat and let the soup simmer uncovered for about 5 minutes.

Remove the pot from the heat completely before stirring in your shredded cheddar cheese.

Fold in your reserved chopped broccoli at this point.

Taste your soup and season with salt and pepper as needed. Serve immediately while it's warm and at its creamiest.