Add the poblano peppers to a baking sheet and place them directly under the broiler. Broil for 5 minutes on each side until the skin is blackened and blistered.

Remove the peppers from the oven, cover them with aluminum foil, and allow them to steam and the skin to soften for about 5 minutes.

Carefully peel off and discard the skin from the poblanos. Make a slit down the middle and scoop out the stem, ribs, and seeds. Dice the peppers and set aside.

Melt the butter in a large skillet or sauté pan over medium heat. Add the onion and cook until softened, about 6-8 minutes. Stir in the garlic and cook for an additional 30 seconds until fragrant.

Reduce the heat to medium-low and add the milk and cream cheese. Stir continuously until the cream cheese has fully melted.

Stir in the salsa verde until fully combined.

Add the cheese cubes a handful at a time and continuously stir into the heated mixture with a whisk until they are fully incorporated and melted. Continue this process until all the cheese cubes are melted, making sure to gently and continuously whisk the queso dip until it is smooth and silky.

Stir in the diced roasted poblano peppers, remove from the heat, and serve immediately with tortilla chips.