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Heat 3 Tbsp. extra-virgin olive oil in a large skillet over medium. Cook 1 medium onion, finely chopped, and 4 garlic cloves, finely grated, stirring often, until onion is softened and fragrant, about 4 minutes. Add ⅓ cup double-concentrated tomato paste, 2 Tbsp. chili powder, 1 Tbsp. unsweetened cocoa powder, 2 tsp. smoked paprika, and ½ tsp. cayenne pepper and cook, stirring constantly, until paste starts to stick to bottom of pan, about 2 minutes. Stir in 2 tsp. all-purpose flour, then gradually pour in 1¾ cups low-sodium vegetable broth, whisking constantly. Bring mixture to a simmer.
Add juice of 1 medium lime, 2 Tbsp. dark brown sugar, and 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt and stir until sugar and salt are dissolved. Add 1½ lb. large shrimp, peeled, deveined, and cook, stirring constantly, until just opaque and slightly curled, about 5 minutes. Taste shrimp mixture and season with more salt if needed. Remove from heat.
Top shrimp mixture with cilantro leaves and serve with tostadas and lime wedges for squeezing over if desired.