Melt butter and cook onion and garlic for 3 to 4 minutes until soft and fragrant

Add broccoli, broth, and thyme, then cover and simmer about 6 minutes until tender

Stir in cream cheese and simmer 2 minutes until melted

Remove 1 cup vegetables, chop, and set aside

Blend remaining soup until smooth and creamy

Add heavy cream and bring to a gentle boil

Reduce heat and simmer uncovered about 5 minutes until slightly thickened

Remove from heat, stir in cheddar cheese and reserved vegetables until melted

Season with salt and pepper and serve warm