Combine chili paste, white vinegar, rice vinegar, garlic cloves, kosher salt, sugar, and water in a saucepan and bring to a boil. Simmer for 30 minutes and skim if needed. Add cornstarch and bring back to a boil to thicken. Set aside and let cool.
Heat oil to 360 degrees F. in a deep pot.
Dredge crab in buttermilk and dip in tempura flour. Fry in oil for 2 minutes until crisp. Set aside. Place asparagus spear in oil for one minute. Set aside.
Place 2 ounces of the cooled chili paste sauce in a shallow bowl along with a mound of cooked rice noodles. Arrange carrot and sprigs of basil, cilantro, and mint next to the noodles. Place lime wedge along side the noodles. Put fried crab on top of noodles with asparagus spear.
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