Heat 2 tablespoons of the neutral oil in a large, straight-sided skillet over medium heat until shimmering. Add 1/2 cup panko breadcrumbs and 1/2 cup sweetened coconut flakes and cook, stirring frequently, until golden-brown, about 4 minutes. Transfer to a small bowl. Season with 1/4 teaspoon of the granulated sugar and 1 pinch kosher salt, and toss to combine.
Pat 1 pound raw extra-jumbo shrimp dry with paper towels and season with 1/2 teaspoon of the kosher salt. Heat the remaining 1 tablespoon neutral oil in the same skillet (no need to clean) over medium-high heat until shimmering. Add the shrimp in a single layer and cook until starting to brown on the bottom and they release easily from the pan, about 2 minutes. Flip the shrimp and cook until just cooked through, about 1 minute more. Transfer to a bowl or plate.
Add 1 (about 13-ounce) can coconut milk, 3 cups water, 12 ounces dried spaghetti or linguine, 1 pint cherry or grape tomatoes, remaining 1 1/2 teaspoons kosher salt, and remaining 1/4 teaspoon granulated sugar to the skillet. Finely grate 2 garlic cloves directly on top.
Bring to a boil over high heat. Continue to boil, turning the pasta frequently with tongs, until the pasta is al dente and the liquid has nearly evaporated, 8 to 11 minutes. Meanwhile, pick the leaves and tender stems from 6 fresh cilantro sprigs and finely chop (about 1 tablespoon).
Remove the skillet from the heat. Add 3 ounces baby spinach and toss until wilted. Finely grate the zest of 1 medium lime directly into the skillet. Halve the zested lime; squeeze the juice from one half into the skillet and cut the remaining half into wedges. Toss the pasta to combine. Taste and season with more kosher salt as needed.
Top the pasta with the shrimp, then sprinkle with half of the panko mixture. Garnish with the cilantro and serve with lime wedges and the remaining panko mixture on the side to add as you eat.