Thinly slice mushroom caps; discard stalks.

Melt butter in a heavy-bottomed pan. Add green onions, garlic, and 1 teaspoon lemon thyme leaves. Cook and stir for 1 minute, or until garlic is golden.

Add mushrooms, salt, and pepper; cook for 3 to 4 minutes, or until mushrooms begin to soften. Add flour and cook, stirring constantly, for 1 minute.

Remove from the heat and add broth, stirring continuously. Return to the heat and stir until boiling. Reduce the heat and simmer gently for 2 minutes, stirring occasionally.