Preheat your oven to 450°F (232°C). Line a baking sheet with foil.

Place the Hatch chiles on the prepared baking sheet and roast in the oven for 10-15 minutes, turning occasionally, until the skins are blistered and charred.

Remove the chiles from the oven and transfer them to a bowl. Cover the bowl with plastic wrap or a lid and let them steam for 10 minutes to loosen the skins.

Peel the charred skins off the chiles, remove the stems, and discard the seeds. Chop the chiles into small pieces and set aside.

Heat the olive oil in a large skillet over medium heat. Add the onion and sauté for 4-5 minutes, until softened and translucent.

Add the garlic to the skillet and cook for 1 minute, stirring frequently to prevent burning.

Add the chopped Hatch chiles to the skillet, followed by the chicken broth, cumin, oregano, salt, and black pepper. Stir to combine thoroughly.

Bring the mixture to a simmer and let it cook for 10 minutes, stirring occasionally, until the sauce thickens slightly.

Remove the skillet from heat and stir in the lime juice. If desired, stir in the chopped cilantro for added freshness.

Use the sauce immediately as a topping for enchiladas, tacos, or grilled meats, or let it cool and store in an airtight container in the refrigerator for up to 5 days.