Step 1

Stir masa, 1 Tbsp. lard, 1 tsp. Diamond Crystal or ½ tsp. Morton salt, and 1 cup water in a medium bowl until a soft and slightly sticky dough forms. If dry, mix in another 1 Tbsp. water. Cover and let sit at least 30 minutes and up to 3 hours.

Step 2

Meanwhile, bring guajillo chiles, morita chiles, coriander, and 1½ cups water to a boil in a small saucepan. Cover, remove from heat, and let sit, stirring occasionally, 30 minutes to allow chiles to soften. Transfer to a blender and purée until smooth; set aside.

Step 3

Place rack in lowest position in oven; preheat to 500°. Brush a rimmed baking sheet with 2 Tbsp. lard. Divide dough into 4 pieces and form into balls. Set on work surface and cover with a damp kitchen towel. Place 1 ball between 2 sheets of parchment or wax paper. Using a small skillet or saucepan, gently press ball into a 5"-diameter disk. Carefully peel away parchment; place on prepared baking sheet. Repeat with remaining balls.

Step 4

Bake gorditas until outer edges are lightly golden, 10–12 minutes. Turn over and bake until golden brown and crisp, 10–12 minutes. Transfer to plates and let cool 10 minutes. Insert a paring knife into side of gordita and, using a slow sawing motion, cut open along one side (keep other side intact).

Step 5

Heat remaining 2 Tbsp. lard in a large skillet over high. Cook shrimp until lightly browned and just cooked through, about 1 minute per side. Transfer to a medium bowl. Reduce heat to medium and cook garlic in same skillet, tossing often, until beginning to brown, about 1 minute. Add thyme sprigs, vinegar, agave, 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt, and reserved chile purée. Cook, stirring occasionally, until brick red and the consistency of a thick sauce, 6–8 minutes. Add shrimp and any juices and cook 1 minute. Remove from heat; add butter and stir constantly until melted and sauce is glossy. Season with more salt if needed. Remove and discard thyme.

Step 6

Fill gorditas with shrimp mixture, onion, avocado, and cilantro. Serve with lime wedges for squeezing over.