Prepare jars, two-piece lids, and hot water canner for canning.

Using a sharp serrated or regular paring knife, halve and core the tomatoes.

Coarsely chop the tomatoes with a knife or pulse in batches in a food processor. Add the chopped tomatoes to a large heavy-bottomed pot as you work.

Add sugar, cinnamon, cloves, and lemon slices to the chopped tomatoes.

Bring the contents of the pot to a boil over medium-high heat. Boil for 25 minutes, stirring more and more frequently to prevent scorching as the tomatoes break down and begin to thicken.

Reduce heat to low and simmer the green tomatoes for 30 minutes, stirring frequently, or until the jam begins to thicken up. Remove from the heat. (If you've used a cinnamon stick instead of ground spices, remove it before ladling into jars.)

Using a funnel and a ladle, carefully decant the hot tomato jam into the prepared jars leaving 1/4-inch headspace (make sure they're still hot to prevent breakage from thermal shock). Remove air bubbles with a wooden chopstick or plastic knife, adding more jam if needed to reach headspace requirements.

Wipe the rims and sides of the jar down with a clean cloth and apply two-piece lids until fingertip tight.*

Load the jars into a hot water canner and add 2 tablespoons of distilled white vinegar to the water. Make sure the jars are covered with at least 1 inch of water.

Bring the canner to a boil and set a timer for 20 minutes. When the timer goes off, turn off the heat and give the jars another 5 minutes in the hot water before removing them.

Place the jars on a clean tea towel, leaving 1 inch of space between each jar. Let the jars cool down completely to room temperature and check the seal on each jar. Move any unsealed jars to the fridge. Remove the band from sealed jars for future canning projects.

Store canned green tomato jam in a cool, dry place away from direct sunlight for up to 18 months.