In a medium saucepan over medium heat, melt butter, then add onion & cook 5 minutes or until softened, stirring often.
Add garlic, thyme & lemon pepper, cooking another minute while stirring.
Sprinkle in the flour, stirring constantly until flour is incorporated.
Slowly add the broth, 1/2 cup at a time, stirring to blend.
Add broccoli & cook 10 minutes or until tender.
Carefully transfer 1/2 to 3/4 of the hot mixture to a blender (depending on how chunky or smooth you want the finished soup) & blend until smooth, then, in the saucepan, reincorporate the blended mixture with that which wasn't blended.