Slice your hatch chiles and tomatoes in half lengthwise, then scoop out the pepper seeds if you want a milder salsa. Cut the onion into large chunks so it roasts without turning mushy. Leave the garlic cloves in their skins for now, since roasting them whole keeps them from burning.
Preheat your oven to 350°F and arrange the peppers, tomatoes, onion, and garlic cut-side up on a baking sheet. Drizzle everything lightly with olive oil so the skins char nicely instead of drying out. Roast for 20-25 minutes, until the pepper skins are blistered and blackened in spots.
Once out of the oven, let everything rest for about 10 minutes until it's cool enough to handle safely. Peel the charred skins off the hatch chiles and tomatoes, then discard them, since this step is what gives the salsa its silky texture. Squeeze the softened garlic cloves out of their papery skins directly into your food processor.
Add the roasted peppers, tomatoes, onion, and garlic into the food processor along with the lime juice, cilantro, and salt. Pulse a few times for a chunkier texture, or blend longer if you prefer a smoother, restaurant-style salsa. Taste and adjust the salt or lime as needed before moving on.
Transfer the salsa into a covered bowl and refrigerate for at least 2 hours before serving. This resting time lets the smoky, roasted flavors fully develop and meld together. Serve it cold or at room temperature alongside your favorite dish.