This slightly smoky sauce has a nice background note of heat. It's a perfect complement to lamb, beef, chicken or roasted vegetables.
Roast tomatoes in a heavy dry skillet, such as cast-iron, over medium heat, turning, until blistered all over and blackened in spots, about 5 minutes. Transfer tomatoes to a cutting board and cover with a kitchen towel to steam. When cool, peel and coarsely chop.
Meanwhile, toast chiles in the same pan over medium heat until fragrant, 20 to 30 seconds per side. Let cool and tear into several pieces.
Heat oil in a medium saucepan over medium heat. Add onion and shiitakes and cook, stirring often, until tender, 2 to 3 minutes. Add garlic and oregano and cook for 30 seconds more. Add broth, tomatoes and chiles; bring to a boil. Reduce heat to low and simmer, covered, for 30 minutes.
Transfer sauce to a blender or food processor and puree. Pass through a fine-meshed sieve into the saucepan. Heat through, stirring. Season with lemon juice, sugar, salt and pepper.
Make Ahead Tip: The sauce will keep, covered, in the refrigerator for up to 2 days or in the freezer for up to 6 months. Reheat before serving.
Tip: Be sure to seed the New Mexico chiles; otherwise the sauce will be overwhelmed by their heat.