Halve tortillas. Brush 1 half with some of egg mixture and place 1 piece asparagus along cut side. Tightly roll up tortilla. Insert 1 pick crosswise to secure. Brush outside of roll with more of egg mixture and sprinkle with sesame seeds. Roll remainder of asparagus is same manner.
Heat 1/2 inch of oil in a 10-inch heavy duty skillet to 350°F.
Fry rolls in batches of 3, turning over once, until golden brown, about 3 minutes per batch, returning oil to 350F between batches. Transfer to paper towels to drain.
Stir together remaining ingredients until sugar is dissolved. Serve with rolls.