Cover the rice noodles with very hot tap water in a large bowl and stir to separate. Let the noodles soak until they are softened and pliable but not fully tender, 35 to 40 minutes, then drain. Spread the tofu over a paper towel–lined baking sheet and let it drain for 20 minutes.

Pulse the chiles, garlic, and shallots in a food processor until they form a smooth paste, about 20 pulses. In a separate bowl, whisk together the broth, fish sauce, sugar, and lime juice.

Adjust an oven rack to the upper-middle position and heat the oven to 200°F. Pat the tofu dry with paper towels, season with salt and pepper, and toss with the cornstarch. Shake the coated tofu in a strainer over a bowl to remove any excess starch. Heat 3 tablespoons of oil in a 12-inch nonstick skillet over medium-high heat until the oil just begins to smoke. Add the tofu and cook, turning as needed, until crisp and browned on all sides, 8 to 10 minutes; transfer to a paper towel–lined plate and keep warm in the oven.

Wipe out the skillet with paper towels, add 1 tablespoon of oil, and heat over high heat until just smoking. Add the snap peas and bell pepper and cook, stirring often, until the vegetables are crisp-tender and starting to brown, 3 to 5 minutes; transfer to a bowl.

Add the remaining 3 tablespoons of oil to the empty skillet and heat over medium-high heat until shimmering. Add the processed chile mixture and cook until the moisture evaporates and the color deepens, 3 to 5 minutes. Add the drained noodles and the broth mixture and cook, tossing gently, until the sauce has thickened and the noodles are tender and well coated, 5 to 10 minutes.

Stir in the cooked vegetables and the basil and cook until the basil wilts slightly, about 1 minute. Divide into portions and top with the crispy tofu to serve while hot.