Sauté the aromatics: In a medium saucepan, melt the butter and olive oil over medium heat. Add the chopped onion and sauté for 3–4 minutes until translucent and fragrant. Stir in the minced garlic and cook for another 30 seconds, just until aromatic — don’t let it brown.
Add the flavor base: Stir in the green chiles, tomatillos, and broth. Mix everything together and bring the mixture to a gentle simmer. Let it cook for about 8–10 minutes, allowing the flavors to combine and the tomatillos to soften slightly.
Blend until smooth: Carefully transfer the mixture to a blender or use an immersion blender directly in the pot. Add the cilantro, cumin, salt, and black pepper. Blend until completely smooth and creamy. If the sauce looks too thick, add a splash more broth to loosen it up.
Add the creamy elements: Return the blended sauce to low heat. Stir in the Monterey Jack, cheddar, sour cream, and heavy cream. Keep whisking slowly until the cheeses melt and the sauce becomes silky and smooth. Be patient and stir often — this step creates that rich, velvety texture Chuy’s Boom Boom Sauce is famous for.
Adjust and finish: Taste and adjust seasoning with a pinch more salt or cumin if needed. Continue cooking on low heat for another 2–3 minutes until warm and fully combined. The sauce should be thick enough to coat the back of a spoon but still pourable.
Serve: Pour the hot Boom Boom Sauce into a serving bowl or drizzle it generously over enchiladas, tacos, grilled chicken, or burritos. It also makes an incredible dip for tortilla chips or vegetables. Garnish with a sprinkle of chopped cilantro or crumbled queso fresco if you like an extra Tex-Mex touch.