Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms, onion, and garlic to pan; sauté 10 minutes or until tender. Remove from heat.
Place tofu in a large bowl. Add miso, juice, salt, and pepper; mash with a fork until combined. Add mushroom mixture to tofu mixture in bowl, and stir until combined.
Heat a large nonstick skillet over medium heat. Add 1 bag spinach to pan; cook until wilted (about 7 minutes), stirring frequently. Drain. Repeat procedure with remaining 2 bags spinach. Add spinach to the tofu mixture in bowl; stir until well combined. Cool.
Preheat oven to 400°.
Place 3 phyllo sheets on a large cutting board or work surface (cover the remaining dough to keep from drying); lightly coat phyllo with cooking spray. Cut stack lengthwise into 4 (3 1/2-inch-wide) strips. Spoon about 1 rounded tablespoon spinach mixture onto one end of each strip. Fold one corner of the opposite end over mixture, forming a triangle; keep folding back and forth into a triangle to the end of strip. Place triangles, seam sides down, on a baking sheet. Lightly coat tops with cooking spray. Repeat procedure with remaining phyllo sheets and filling. Bake at 400° for 12 minutes or until golden.