Place peppercorns in a small zip-top plastic bag; seal. Crush peppercorns using a meat mallet or small heavy skillet. Combine peppercorns, salt, and garlic in a bowl; rub evenly over caps that have been lightly sprayed with olive oil cooking spray.
Heat a large nonstick skillet over medium-high heat. Coat pan with olive oil cooking spray. Add caps to pan. Reduce heat; cook 4-5 minutes on each side or until desired degree of doneness. Remove caps from pan. Cover and keep warm.
Add port and broth to pan, stirring to loosen browned bits. Cook until reduced to 1/4 cup (about 3 minutes). Place 2 caps on each plate (over french bread sautéed in vegan butter if you’re not concerned with carbs;); drizzle each serving with 1 tablespoon sauce. Sprinkle each serving with 3/4 teaspoon thyme.