Snap off and discard woody bases from asparagus; trim asparagus. Set aside. If using medium carrots, quarter lengthwise. Cut the large carrot quarters or thinner quarters in half crosswise making long carrot sticks. In a large skillet bring 1 inch of lightly salted water to boiling. Add asparagus; return to boiling. Cook, uncovered, 2 to 3 minutes or until just crisp-tender. Using tongs, remove asparagus from boiling water. Immediately submerse asparagus into a large bowl filled with ice water. Let stand until completely chilled; drain well. Pat dry with paper towels.
Add carrots to boiling water in skillet; return to boiling. Cook, uncovered, 3 to 4 minutes or until just crisp-tender. Remove carrots from boiling water. Immediately submerse in ice water. Let stand until completely chilled; drain well. Pat dry with paper towels. Place drained asparagus and carrots in a self-sealing plastic bag set in a baking dish or a shallow dish thats easily covered.
For vinaigrette in a screw-top jar combine vinegar, oil, snipped fresh tarragon or basil, garlic, 1/2 teaspoon salt, chili paste and 1/4 teaspoon pepper. Cover and shake well. Pour into bag or dish with asparagus and carrots. Add radishes. Seal bag or tightly cover dish and chill 2 to 4 hours, turning bag occasionally.
Transfer mixture to a serving bowl or individual serving glasses. Trim with sprigs of fresh tarragon or small basil leaves. Season to taste with additional salt and pepper. Makes 6 servings.