Combine ingredients in a large saucepan. Bring to a boil, then reduce heat and simmer, stirring frequently until thick (about 1 hour). Ladle hot mixture into pint jars, leaving 1/2-inch headspace. Adjust lids and process in boiling-water canner for 15 minutes at 0–1,000 feet elevation, 20 minutes at 1,001–6,000 feet, and 25 minutes above 6,000 feet.
Preheat the broiler. Put the quartered tomatoes, sliced onion, and whole garlic cloves onto a roasting tray, spreading out evenly. Drizzle with plenty of olive oil and season well with salt and pepper and sprinkle with cilantro sprigs. Broil until everything is nicely charred, about 10 minutes (you want lots of deep rich color so don't be afraid if some of the edges get pretty black).
As you will notice when we dive a little further into these recipes, Mexican food has a stunning range of somewhat special ingredients. From Masa Harina, the essential ingredient of corn over a wide array of chilies either fresh, dried or ground to Mexican oregano and tomatillos. Some of these may at first glance seem foreign and difficult to come by, but fear not we’ll discuss the individual ingredients as we go and they’ll be easier to come by than you think.