Canning tomatoes involves steps such as coring and scoring the tomatoes, blanching and shocking them, and skinning, seeding and crushing them. The tomatoes must be stewed them before being placed in sterilized jars for canning.
Cut out the core from the top of the tomatoes with a small knife, and score an X-shaped cut into the bottoms. Blanch the tomatoes by submerging them in boiling water for 20 to 30 seconds, then immediately removing them to an ice water bath. Peel the skins from the tomatoes, tear them open to remove the seeds and liquid, and crush them in a separate bowl. Place the crushed tomatoes into a pot, simmering until they break down.
Fill a pressure canner to the 3-quart line, and set on high heat. When the water reaches 180 degrees Fahrenheit, sterilize everything by submerging the jars, lids, and rings from mason jars along with a funnel, ladle, and jar tongs into the water. Keep everything in a preheated oven at 220 degrees Fahrenheit until ready to use.
To can, stuff a sprig of basil into each jar, and ladle in the cooked tomatoes using a funnel. Leave about 1/2 inch of open space at the top. Use a narrow object to dislodge any air bubbles, and wipe the rims clean. Screw the lids on top until tight. Place the jars back in the canner for about 15 minutes at a constant 11 pounds of pressure before removing and allowing to cool.