In a medium saucepan over medium heat, melt the butter until foamy. Whisk in the flour and cook 30–45 seconds to form a light roux, stirring constantly so it doesn't brown.

Add dairy

Slowly whisk in the whole milk and half-and-half until smooth. Bring the mixture to a gentle simmer, stirring frequently, until it thickens slightly, about 3–4 minutes.

Melt cheese

Reduce heat to low. Add the shredded white American and Monterey Jack cheeses in batches, stirring and allowing each addition to melt before adding more. Keep the sauce on low to avoid separating; do not boil.

Season and finish

Stir in the minced garlic, drained diced green chiles, ground cumin, lime juice, salt, and pepper. Taste and adjust seasoning. If the queso is too thick, stir in up to 2 tablespoons more milk, 1 tablespoon at a time, to reach a smooth dipping consistency. Keep warm on the lowest heat or transfer to a small fondue-style warmer or slow cooker set to warm.

Pico de Gallo

Combine the diced tomatoes, finely diced yellow onion, chopped cilantro, and minced jalapeño in a bowl. Add the lime juice, salt, and pepper and gently toss to combine. Let the pico rest for at least 10 minutes at room temperature to allow flavors to marry; taste and adjust seasoning (more lime or salt) if needed.

Garnish & Serve

Spoon the warm queso into a shallow serving bowl. Spoon the pico de gallo over the center of the queso, leaving some cheese visible around the edges for dipping.

Scatter the thinly sliced green onions over the pico and queso. Place tortilla chips on a platter around the bowl. Serve immediately with lime wedges on the side for squeezing over chips or pico as desired.

Storage: If holding queso for later, cool to room temperature and refrigerate in an airtight container up to 3 days. Reheat gently over low heat, stirring and adding small amounts of milk to restore creaminess. Store pico separately up to 24 hours refrigerated.