1/4 cup (about 1 cup) finely grated reggiano cheese
Fresh thyme leaves
Make Crust Sponge:
In a bowl, stir yeast into warm water. Set aside briefly, until yeast begins to foam. Add 4 cups flour, flax meal, and 1/2 cup cold water; mix thoroughly. Cover bowl with a towel and set aside in a warm place 2-3 hours.
Add remaining tablespoon flour and remaining tablespoon cold water; mix thoroughly. Cover with a towel and set aside for additional 2-3 hours. (Sponge can be made a day before the crust is completed.)
Place flour in large mixing bowl or bowl of stand mixer with dough hook.
In a small bowl, mix warm water and honey. Stir in yeast. Set aside briefly, until yeast begins to foam. Stir in cold water. Pour mixture into the flour and add sponge. Mix. If mixing by hand, remove mixture from bowl and place on counter surface; knead 5-6 minutes. Add salt and knead another 2 minutes, adding more flour if necessary to form an elastic dough. Knead in olive oil until incorporated. If using a mixer, mix/knead until dough is elastic.
Divide dough in half. Form into two tight balls. Set in a deep pan with 2-3 inches space around each ball; cover. Refrigerate 24-48 hours. Remove dough from refrigerator. Place in warm spot and allow the dough to proof (rise). Meanwhile, make the topping.
Pour boiling water over dried mushrooms to cover. Let stand 10-15 minutes.
In large sauté pan, heat butter and oil over high. Add onions; reduce heat to medium-low and sweat onions a few minutes. Add garlic, shallots, sugar, and salt. Continue cooking another five minutes. Drain mushrooms; add to pan. Stir. Add sherry; cook 10 minutes. Add Worcestershire, soy sauce, a few dashes of Tabasco® sauce and herbs. Salt and pepper to taste. Remove from heat. Reserve.
Mix together a spoonful of semolina with a spoonful of all-purpose flour; spread over a flat surface and push 1 dough ball into a 10-12 inch circle, allowing enough dough to form a lip. Repeat with second dough ball.
Divide mozzarella over the crusts. Sprinkle 1/2 cup grated Le Gruyère cheese over each crust. Divide onion/mushroom topping over each and sprinkle remaining Gruyère over, 1/2 cup each.
You can cook the pizza, according to your preference. Grill crusts first on hot grill; then add toppings and continue to grill (450-500 F°) OR top the unbaked crusts and bake in wood-fired oven (700-800°F).