Start by melting the butter in a medium saucepan over medium heat. Add the diced shallot and sauté until translucent, about 3-4 minutes. Next, add the minced garlic and diced jalapeños, stirring for another minute until fragrant.
Pour in the half & half (or evaporated milk) and bring the mixture to a gentle simmer. Stir occasionally to prevent it from scorching.
Add the diced chipotle chiles and sprinkle in the corn starch. Whisk continuously until the mixture thickens slightly, about 2-3 minutes.
Add in the softened cream cheese and yellow mustard. Stir until the cream cheese is fully melted and incorporated into the sauce.
Gradually add the smoked cheddar and sharp cheddar cheese, stirring constantly until all the cheese is melted and the queso is smooth and creamy.
Remove from heat and serve warm with tortilla chips, over nachos, or as a topping for your favorite dishes. Don’t forget to garnish with fresh cilantro or diced tomatoes for an extra pop of color!