When the water in the canner is at least 180 degrees Farenheit but not quite boiling, submerge your jars, lids, rings, funnel, ladle and jar tongs (a lid caddy is a handy tool for this). If you are preparing a large number of jars, you can run them through the dishwasher (provided it sterilizes), then keep in a 220 degrees Farenheit oven until ready. Keep everything hot until just before you're ready to can.
Remove as many jars, lids, etc., as you will can at once (a 23-quart canner can handle seven quart jars). Stuff a sprig of basil into each jar, if desired. Ladle the tomatoes through the wide-mouth funnel into each jar, leaving about 1/2" headroom at the top.
Insert a clean spatula, knife or chopstick, and "bubble" the contents, wiggling it around the perimeter to dislodge any air bubbles. Using a wet paper towel, wipe the rims of the jars clean, then set the lids on top. Apply the rings, screwing on until just finger-tight. Using the tongs, lower the jars into the canner and close the lid. Keep over high heat until steam flows freely through the vent at the top; continue venting for 10 minutes, then apply the valve. Keep over high heat, monitoring the pressure. When the pressure hits 11 pounds, reduce the heat to low and set the timer for 15 minutes. Keep an eye on the pressure: It can go over 11 pounds, but it's best to keep the pressure as stable as possible. Moreover, if it dips below 11 pounds, it must be brought back up, and the 15 minutes started again.
When the 15 minutes are up, kill the heat and allow to cool naturally. When the pressure has fallen completely and the cover lock drops, open the canner and remove the cans with your tongs to the cooling racks. Once cool, several hours later, test the jars by removing the rings and lifting the jars by the lids. If the lids give, the seal did not set. These may be refrigerated and used right away, or the tomatoes can be reprocessed and canned using the above instructions.
Some separation may occur as the jars cool, especially for the tomato water; this is normal. Puree may retain its emulsion better.
Sean Timberlake is a professional writer, amateur foodie, avid traveler and all-around bon vivant. He is the founder of Punk Domestics, a content and community site for DIY food enthusiasts, and has penned the blog Hedonia since 2006. He lives in San Francisco with his husband, DPaul Brown, and their hyperactive terrier, Reese. Sean is also a regular contributor on Cooking Channel's Devour. Check out his blog posts here.