Sauté onion, garlic, cumin, cayenne, and salt in butter until fragrant, 4 min.
Simmer 1¾ cups milk; whisk in cornstarch slurry (¼ cup milk + cornstarch) and cook 1 min.
Melt American cheese over low heat, 3 min; stir in Monterey Jack gradually, 4 min.
Off heat, stir in jalapeños and pickle juice; season to taste.
Serve warm with tortilla chips.