Get your canning set-up arranged with jars sterilized and simmering in your water bath canner, lids hanging out in warm water, and all your gear together.
Cover a sheet pan with foil and place tomatoes and onions, cut side down on it. Broil the veggies until the tomatoes are well charred (anywhere from 10-15 minutes). Remove the pan from the oven and offload the veggies into a bowl. Add the jalapenos, cut side down, and garlic to the empty sheet pan and broil until jalapenos are also charred, 8-10 minutes.
Transfer the jalapenos, garlic, half of the tomatoes, and half of the onions to food processor and pulse until it's a thick puree. Transfer to Dutch oven. Transfer remaining broiled tomatoes and onions to the food processor and pulse into ½-inch pieces, 2 or 3 pulses; add to Dutch oven.
Stir in lime juice, salt, sugar, cilantro, and cumin. Boil over medium-high heat, stirring often, until salsa has thickened slightly, probably 8-15 minutes depending on your stovetop.
Ladle the hot salsa into the hot jars, leaving ½ inch headspace. Use a wooden skewer or popsicle stick to remove air bubbles. Wipe rims clean, top jars with warm lids, screw on bands until fingertip tight, and return jars to canner.
Bring water in canner back to a boil. Process jars for 15 minutes for up to 1,000 feet, 20 minutes for 1,001 to 3,000 feet, 25 minutes for 3,001 to 6,000 feet, or 30 minutes for 6,001 to 8,000 feet. Remove jars to a cooling rack and let sit undisturbed for at least 8 hours. Check seals and store. If any failed to seal (hey it happens to even the most experienced canner), grab some chips and have a movie party. Don't forget to label them, and you can decide yourself if sharing is caring. According to Bear, that would be hard no.