Stir broth, 3 tablespoons bourbon, sugar, and vinegar in small bowl until sugar dissolves. Sprinkle pork with salt, pepper, and allspice. Melt butter in medium nonstick skillet over medium-high heat. Add pork. Sauté until just cooked through, about 4 minutes per side (butter will brown). Transfer pork to platter.
Add bourbon mixture to skillet and bring to boil. Add sugar snap peas and cook until crisp-tender, about 2 minutes. Using slotted spoon, scatter peas over pork. Remove skillet from over heat. Add remaining 3 tablespoons bourbon to sauce in skillet. Boil over high heat until sauce is reduced to thin glaze and coats spoon lightly, about 3 minutes. Mix in mint; spoon over pork and serve.