Heat the olive oil in a medium skillet over medium-high heat. Add the chopped onion and cook for about five minutes, stirring occasionally, until it turns soft and translucent. Stir in the garlic during the last minute and cook just until it smells fragrant, taking care not to let either one brown.
Transfer the softened onion and garlic straight into a food processor. Add the fire-roasted hatch chiles and pulse eight to ten times until everything forms a rough, thick paste. I don't fully puree it at this stage, since it blends smoother once the wet ingredients go in.
Add the chopped cilantro, lime zest, lime juice, cider vinegar, honey and salt to the food processor. Puree everything until smooth, stopping once or twice to scrape down the sides. This is where the sauce really comes together into that glossy, pourable texture.
Give the sauce a taste before you call it finished, since hatch chiles can range from mild to seriously spicy. If it needs more brightness, add a touch more lime juice; if it tastes too sharp, a little extra honey mellows it right out.
If you'd like a thinner, more pourable sauce, add a tablespoon or two of hot water and pulse again to combine. I do this when I'm using the sauce as a marinade or drizzling it over eggs, since a looser consistency spreads more easily.
Transfer the finished sauce to an airtight container and refrigerate it until you're ready to use it. It's ready to eat right away, but I think the flavors settle in nicely after an hour or two in the fridge.