Start by heating a large skillet over medium heat. Add your choice of sausage and cook, breaking it apart with a spatula until fully browned and cooked through, about 6-8 minutes. Next, add the diced sweet onion and cook until translucent and soft, about 3-4 minutes. Season with 1/4 teaspoon salt, stir to combine, and remove from heat. Set aside.
In a medium saucepan, melt the unsalted butter over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant but not browned. In a small bowl, whisk together the half and half and cornstarch until smooth. Slowly pour this mixture into the saucepan, whisking constantly. Cook until the mixture thickens slightly, about 3-4 minutes.
Reduce heat to low and gradually add the freshly grated sharp white cheddar and Monterey Jack cheeses to the sauce, stirring continuously until fully melted and smooth. Season the cheese sauce with 1/8 teaspoon salt and 1/8 teaspoon pepper. Keep the sauce warm on low heat.
Add the cooked sausage and onion mixture into the melted cheese sauce. Stir gently to combine all the ingredients evenly. Taste and adjust seasoning if necessary.
Warm both the soft flour or corn tortillas and the hard-shell corn tortillas according to package instructions or over a dry skillet until pliable and fragrant.
Spoon a generous amount of the cheesy chorizo mixture onto each tortilla. Top with chopped fresh cilantro and a squeeze of fresh lime juice to brighten the flavors.
Serve immediately while warm. These Queso Fundido Tacos pair wonderfully with fresh sides or you can try a creative twist like using Zucchini Corn Fritter Taco Shells for a unique base.