In a large saucepan, melt butter over medium heat and then add onion and carrots and cook for about 3 minutes or until softened.

Add to the saucepan, the vegetable or chicken broth, broccoli, thyme, garlic powder, and salt/pepper. Simmer until broccoli is softened, about 6-8 minutes.

Remove 1 cup of the vegetables to set aside. Using either an immersion blender or regular food blender, blend remaining ingredients together. If using a food blender, add ingredients back to the saucepan and bring to a simmer.

Place flour in a bowl. Add in milk a little at a time whisking until smooth.

Whisk in the flour and milk mixture to the ingredients in the saucepan. Turn heat up slightly and continue whisking until thick and bubbly, about 3-4 minutes.

Remove from heat, add in lemon juice, stir in cheese and reserved chopped vegetables and serve immediately.