Creamy Leeks + Black Trumpet Mushrooms on Toast

In a large cast iron skillet or dutch oven, melt 2 tablespoons of butter over medium heat. Add garlic and leeks. Move around the pan to cook 1-2 minutes.
Add chicken broth, cream, wine, and thyme. Let simmer 10 minutes, uncovered. Season with salt and pepper. Cover and turn heat to low to keep warm.
Cover the bottom of a baking sheet with aluminum foil and place the slices bread in a single layer on top. Butter each with 1/2 tablespoon butter.
Place two slices of mozzarella cheese on each and set aside (turn the oven broiler on).
Remove thyme sprigs from the leek mixture and add the mushrooms, turn heat back up to medium and cover, 1-2 minutes.
In a separate skillet on medium-high heat, add 1 tablespoon butter and cook 4 eggs over-easy.
Give trumpet mushrooms a stir to mix in with leeks and re-cover. Remove from heat.
Broil toast with cheese on it, for approx. 3 minutes or until cheese just barely starts to turn brown and bubble. Remove toast from broiler.
On each plate, place the toast, then an egg over-easy and then the mushroom mixture.