In a small bowl, whisk together the peanut butter and hot water until smooth and well combined. Add the chili oil, soy sauce, minced garlic clove, sugar, and rice vinegar, stirring until the sauce is creamy and fully incorporated. Taste and adjust seasoning as needed. Set aside at room temperature—this sauce can be made up to 2 hours ahead.
Pat the shrimp dry and season with kosher salt and cracked black pepper. Heat a large skillet over high heat and cook the shrimp for about 2 minutes per side until they turn pink and are just cooked through—don't overcook or they'll become rubbery. Transfer to a plate to cool. While the shrimp cooks, bring a pot of water to a boil, add the rice vermicelli, and cook according to package directions. Drain and rinse thoroughly with cold water to stop the cooking and remove excess starch. Spread the noodles on a plate to cool completely.
In a medium bowl, combine the minced garlic cloves, sugar, fish sauce, and lime juice, stirring until the sugar dissolves. Add the bean sprouts, julienned carrot, and thinly sliced scallions, tossing gently to coat everything evenly with the dressing. I prefer to let this sit for just a few minutes so the vegetables absorb the flavors—it makes each bite more vibrant.
Fill a shallow bowl or plate with warm water. Working with one rice paper wrapper at a time, submerge it in the warm water for about 5 seconds—it should still have a slight resistance and not be completely soft. Place the softened wrapper on a clean, dry work surface. Lay a small handful of the cooked rice vermicelli from Step 2 in the center of the wrapper, leaving space on the sides. Top with 2-3 pieces of cooked shrimp, a small portion of the vegetable mixture from Step 3, and a few leaves each of Thai basil, cilantro, and mint. I like to arrange the shrimp pieces in a line so they're visible through the wrapper when rolled—it looks beautiful on the plate.
Fold the left and right sides of the wrapper over the filling, then tightly roll from the bottom up, keeping the sides tucked in as you go. Place the roll seam-side down on a serving plate. Repeat with the remaining wrappers and filling. Serve the rolls immediately with the peanut sauce from Step 1 on the side for dipping. I find that summer rolls taste best served right after assembly while the wrappers are still slightly pliable and the textures are at their best.