Preheat an oven to 400̊ F.
Heat the olive oil in a large skillet over medium-high heat. Add the garlic and continue to cook, stirring constantly for 1 minute. Add the mushrooms, thyme and sage and cook, stirring occasionally. The mushrooms will give off their liquid. Cook, stirring occasionally, until the liquid has evaporated and the mushrooms are soft, 7 to 8 minutes. Season with salt and pepper. Remove them from the pan and cool.
Ten minutes before serving, place one sheet of the lavash on a baking sheet. Repeat with a second sheet of lavash. Bake the two pieces of lavash in the oven until the lavash is light golden. Remove from the oven and spread one-quarter of the mushrooms onto the top of each lavash to ½-inch in from the edge. Top each with one-quarter of the Montasio and one-quarter of the gorgonzola. Bake in the oven until the edges are light golden color, the lavash is crisp and the cheese is melted, about 2 to 3 more minutes.
Remove from the oven and sprinkle each with one-quarter of the chives.
Repeat with the remaining ingredients making 4 lavash pizzas total.