In a medium-size saucepan, over medium heat, add the garlic, shallots, leeks, onion and thyme. Sweat in the butter until fragrant.
Add the broccoli stem slices and saute until softened.
Pour in the chicken stock and bay leaf and simmer for about 20 minutes.
In the meantime, blanch the broccoli tips in a pot of boiling water over medium heat until bright green. Remove the tips from the water and "shock" in a bowl of iced water.
Drain the green tips and puree in a blender. Set aside.
Puree the soup in a blender and strain through a fine chinoise into a large serving bowl.
Add the green tip puree and season with salt and pepper, to taste.
Serve piping hot.