Set a rack in the oven as close as possible to the broiler. Preheat broiler on high.

Place hatch chiles, shallots, garlic, and cherry tomatoes on a rimmed baking sheet. Set the baking sheet under the broiler and cook until everything is nicely blackened all over. Take the pan out occasionally and flip the vegetables to ensure even blackening. This process took me almost 20 minutes.

Take the pan from the broiler and set aside the hatch chiles and garlic. Place remaining vegetables in a food processor and let cool. Once the chiles and garlic are cool enough to handle, remove the stems from the chiles and slice open. Scrape out seeds and set them aside. Place the chiles in the food processor. Peel the skins from the garlic. Discard skins and place garlic in with the rest of the vegetables.

Once cooled, pulse the vegetables a few times, then add sherry vinegar, lime juice, kosher salt and water. Continue pulsing until everything is well combined. The mixture should be chunky.

Next, taste for seasoning. If you feel that the flavors need a little lift, add more salt (I added a few more pinches) and lime juice. If you want to bump up the heat level of the salsa, gradually add hatch chile seeds (I added about 3/4 of the reserved seeds). If you find that your salsa is too thick, thin out with a little water. Store salsa in the refrigerator for 2 to 3 weeks.