For dipping sauce, combine vinegar, mustard, pepper, and salt in a blender container or food processor bowl. Cover and blend or process until combined. With the blender or processor running, slowly add oils in a thin, steady stream. Continue blending or processing until mixture is thick. Transfer to a covered container, and refrigerate up to 4 hours.

Snap off and discard woody bases from asparagus. If desired, remove tips and strings from sugar snap peas. Bring 1 inch of lightly salted water to boiling in a large, deep skillet; add asparagus. Reduce heat and simmer, uncovered, about 4 minutes or until crisp-tender. Using tongs, transfer asparagus to a large bowl of ice water to cool quickly. Add peas to simmering water and cook about 2 minutes or until crisp-tender. Drain and transfer to bowl of ice water.

To serve, transfer sauce to a serving bowl on a platter. Arrange asparagus and sugar snap peas around sauce bowl. Makes 12 servings.

After cooling vegetables in ice water; drain. Cover and chill up to 4 hours.