To prepare dipping sauce, combine first 7 ingredients. Cover and refrigerate.
To prepare dumplings, combine pork and next 10 ingredients (pork through black pepper) in a large bowl.
Working with 1 won ton wrapper at a time (cover remaining wrappers with a damp towel to keep from drying), spoon about 2 teaspoons pork mixture into center of each wrapper. Moisten edges of wrapper with water; bring 2 opposite corners to center, pinching points to seal. Bring remaining 2 corners to center, pinching points to seal. Pinch 4 edges together to seal. Place dumplings, seam sides up, on carrot slices (cover loosely with a damp towel to keep them from drying).
Arrange half of dumplings in a single layer in a bamboo or vegetable steamer. Steam dumplings, covered, for 10 minutes. Remove dumplings from steamer; place on a platter. Keep warm. Repeat procedure with remaining dumplings. Serve with dipping sauce.
Note: If you don't have a steamer, use a heat-proof plate. Set it on top of a heat-proof bowl placed in the bottom of a pot filled with 2 inches of water. Cover and steam.