Heat a medium saucepan over medium heat and add 1 tablespoon unsalted butter. When the butter is melted, add 2 cloves garlic, minced, and cook, stirring, about 60 seconds until fragrant. Add 1/8 teaspoon salt and 1/8 teaspoon pepper and stir to combine.
Slowly stream in 1 cup of the half and half while whisking constantly.
In a small bowl, whisk together the remaining 1/2 cup half and half and 1 tablespoon cornstarch until smooth and lump-free. Stir this slurry into the saucepan and cook, whisking, about 1 minute, until the mixture thickens. Reduce the heat to low.
Add the grated cheeses—16 ounces sharp white cheddar and 8 ounces Monterey Jack—a small handful at a time, stirring after each addition until fully melted and the sauce is smooth. Keep the queso warm over the lowest heat, stirring occasionally.
Meanwhile, heat a large skillet over medium heat. Add 1 pound chorizo and cook, breaking it apart with a wooden spoon and stirring often, until browned and cooked through, about 6 to 8 minutes. Transfer the cooked chorizo to a bowl and set aside.
In a small bowl, combine 1/2 sweet onion, diced, 1/4 cup chopped fresh cilantro, the juice of 1 lime, and 1/4 teaspoon salt. Stir to combine and set aside.
Warm the 84-inch flour or corn tortillas briefly until pliable. To assemble each taco: spread a few tablespoons of the queso on one warmed flour or corn tortilla, wrap that tortilla around one hard-shell corn tortilla, fill the hard shell with crumbled chorizo, and top with the onion–cilantro mixture.
Repeat assembly with the remaining tortillas and ingredients. Serve immediately with any remaining queso on the side.