Pre-heat oven to 425° and line a baking sheet with parchment paper. Whisk together minced garlic, rosemary, 1/4 cup dark maple syrup, maple sugar, dijon mustard, Worcestershire sauce, smoked paprika, salt and pepper.
Add vegetable oil to a large skillet over medium high heat and toss in the mushrooms. Cook the mushrooms for about three to four minutes or until they are nicely wilted and have begun to brown.
Pour the maple mixture over the mushrooms and add the spinach. Continue to cook for an additional five minutes. The mushrooms and spinach will have cooked down and the sauce will have reduce slightly.
Remove from heat. Place the flatbreads on the prepared baking sheet and spoon the mushroom mixture over top. Sprinkle with cheese and place in the pre-heated oven for ten minutes or until the cheese is melted and slightly browned.