Melt 2 Tbsp butter in a medium saucepan over medium heat.
Cook 1 finely chopped small onion until translucent, about 3–4 mins.
Add 3 minced garlic cloves, 2 tsp ground cumin, ½ tsp cayenne, and 1 tsp kosher salt; cook until fragrant, about 30 secs.
Pour in 1¾ cups milk and bring to a bare simmer.
In a small bowl, whisk 1 Tbsp cornstarch with ¼ cup milk until smooth.
Stir slurry into the saucepan and simmer, stirring constantly, until thickened, about 1 min.
Reduce heat to low.
Add 8 oz sliced American cheese, stirring until melted, about 3 mins.
Gradually stir in 8 oz shredded Monterey Jack cheese, one handful at a time, waiting 30 secs between additions, about 4 mins total.
Stir another minute to ensure smoothness.
Remove from heat.
Stir in ⅓ cup chopped pickled jalapeños and 1 Tbsp pickle juice.
Taste and add more salt if needed.
Transfer to a warmed bowl or keep in saucepan over low heat.
Serve immediately with tortilla chips.