Preheat the broiler. Arrange the tomatillos, Roma tomatoes, whole garlic cloves, and serrano peppers on a foil-lined rimmed baking sheet. Lightly drizzle with olive oil. Broil for 8–10 minutes, or until the vegetables begin to blister and char. Remove the garlic cloves, flip the remaining vegetables, and continue broiling for an additional 8 minutes until evenly charred. Remove from the oven and allow to cool.

Once cooled, peel and discard the tomato skins. Remove stems and seeds from the serrano peppers. Transfer the tomatillos, serranos, roasted garlic, kosher salt, lime juice, cilantro, and one roasted tomato to a blender. Blend until smooth and set aside.

Finely dice the remaining roasted tomatoes and combine with the diced Hatch green chiles. Set aside.

In a heavy-bottomed saucepan, melt the butter over medium heat. Add the minced garlic and cook for approximately 30 seconds, or until fragrant. Pour in the half-and-half, followed by the reserved diced tomatoes and Hatch green chiles. Stir to combine.

Add the cubed queso blanco and shredded cheddar cheese. Stir continuously until the cheeses are fully melted and the mixture is smooth. Stir in the salt and half of the prepared salsa verde. Taste and adjust seasoning or add additional salsa verde for increased heat, if desired.

Remove from heat and allow the queso to rest for 1–2 hours to allow flavors to develop. Reheat gently before serving, thinning with additional half-and-half as needed.

Transfer the queso to a serving bowl. Top with guacamole, hot sauce, fresh cilantro, and cotija cheese, if desired. Serve warm with tortilla chips.