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Step 1
Heat olive oil in a large skillet on low heat.
Step 2
Add thinly sliced onions to the pan and sprinkle with about 1/2 teaspoon salt.
Step 3
Distribute onions in an even layer in the pan. Cook until onions are deep golden brown, about 40 - 45 minutes. Stir occasionally.
Step 4
While onions are cooking, prepare the tomatoes. Cut the stem out of each tomato and cut in half horizontally. Scoop out the seeds and pulp from each tomato and dice.
Step 5
When the onions are caramelized, turn the heat on the pan up to medium low. Add the tomatoes, balsamic vinegar, sugar, and remaining 1/2 teaspoon salt. Scrape up any brown bits that have formed on the bottom of the pan.
Step 6
Cook, stirring occasionally, until the tomatoes begin to break down, have thickened and lost most of their moisture, about 30 minutes. (As the tomatoes lose their moisture during cooking, you may need to turn the heat back down to low to keep the mixture from burning.)
Step 7
Taste the jam and add more salt if needed. Likewise, you can also add another splash of balsamic vinegar for extra tang, or another sprinkle of sugar to make the jam a bit sweeter. If you added additional vinegar and/or sugar, allow the mixture to continue cooking for another minute or two for the ingredients to incorporate.
Step 8
Serve immediately with your favorite dish or keep in a sealed container in the fridge for up to 1 week.