Preheat your oven to 450°F (230°C). Place the green chiles and jalapenos on a baking sheet and roast for about 15-20 minutes, turning halfway through, until their skins are charred and blistered. Remove from oven and cover with plastic wrap to steam.
In a large skillet over medium heat, add the olive oil and unsalted butter. Once melted, add the diced sweet onion and sauté for about 3-4 minutes until translucent. Stir in the minced garlic, salt, and pepper for an additional minute until fragrant.
Peel the roasted chiles, remove the seeds, and dice. In a mixing bowl, whisk together the half and half and cornstarch until smooth.
Pour the half and half mixture into the skillet with the sautéed onion and garlic. Stir and bring to a gentle simmer. Gradually add the grated sharp white cheddar and Monterey Jack cheese, stirring continuously until melted.
Fold in the diced roasted chiles and jalapenos. Allow to simmer for an additional 2-3 minutes, stirring occasionally. Add more half and half if too thick.
Transfer the dip to a serving bowl, garnish with fresh cilantro, and serve with homemade tortilla chips. Enjoy!
