Peel asparagus spears from top to bottom with a vegetable peeler, starting below the tips. Cut off woody ends with a knife.
Place asparagus spears in a large, wide saucepan and pour in enough lightly salted water to just cover. Bring water to a boil; add 1 tablespoon butter and sugar. Reduce heat; simmer until spears are tender and easily pierced with a knife, 15 to 25 minutes. Drain well.
Melt remaining 3 tablespoons butter in a small pot over low heat.
Wrap each asparagus spear with a slice of ham. Arrange on a serving plate; drizzle melted butter on top.