Melt 2 Tbsp. butter in large skillet on medium-high heat. Add vegetables and garlic; cook 8 min. or until liquid has evaporated, stirring occasionally. Stir in Gouda cheese, 1 Tbsp. Parmesan and ground red pepper. Remove from heat.
Stack phyllo sheets on clean kitchen towel; spread with mushroom mixture to within 1 inch from one short end of phyllo. Fold 1/2-inch-wide border over filling, then roll dough up, using towel to help roll it up. Place, seam-side down, on baking sheet sprayed with cooking spray.
Melt remaining butter; brush over roll. Sprinkle with remaining Parmesan.
Bake 30 to 35 min. or until golden brown. Cool 5 min. before slicing.