In a large skillet, bring 1/2 in. of water to a boil; add asparagus. Reduce heat; cover and simmer for 2 minutes. Drain and immediately place asparagus in ice water; drain and pat dry.
Wrap a slice of ham around each asparagus spear. Unroll breadstick dough; spread with garlic spread. Cut each breadstick in half lengthwise. Wrap one piece of dough, garlic spread side in, around each ham-wrapped asparagus spear.
Place on an ungreased baking sheet. Bake at 375° for 13-15 minutes or until golden brown. Serve immediately.