Preheat broiler. Place Anaheim and poblano chiles on a foil-lined oven rack and broil 2 - 3 inches from heat source for 10 - 12 minutes or until completely blistered, turning occasionally. Transfer to a bowl of ice water and let stand for 5 minutes. Peel chiles, remove stems, seeds, and membranes, and set aside.

Place butter in a dutch oven (preferably cast iron) and heat over medium heat until melted and beginning to bubble. Add onion and garlic and cook for 6 - 7 minutes or until onion is soft. Add broth and bring to a boil. Add potatoes, oregano, and roasted chiles. Return to a boil, reduce heat, and simmer, uncovered, for 20 minutes. Remove from heat.

One cup at a time, transfer soup to a blender and blend until smooth.

Return puree to dutch oven and add half-and-half, tomatoes, cumin, and salt. Bring to a simmer over medium heat and cook, uncovered, for 8 minutes. Flavors will be at their peak if soup is served immediately.