First of all, purchase the tomato quantity you think you can handle. Making tomato sauce is a challenging task, so don't overestimate yourself.
Preheat the oven to 350 °F (180°C).
Wash the tomatoes. Put them in the sink. Fill it with water, add ½ cup of vinegar and ½ cup of baking soda, wait 10 minutes and rinse.
Cut the tomatoes in half and place them on a baking tray lined with parchment paper - cut open side up.
Season the tomatoes with a tablespoon or two of olive oil, a teaspoon of sugar, a teaspoon of salt, and one tablespoon of chopped basil.
Bake the tomatoes for 40 minutes. Check: a light crust should form on the surface. If not, bake 5-10 minutes more.
Remove the tomatoes from the oven, place them in a large bowl and season them with (quantity for each tray of 2 lbs/1 kg):
2 tablespoons of olives
1 teaspoon of balsamic vinegar
1 tablespoon of capers
1 tablespoon of olive oil
Taste the tomatoes: add whatever of the ingredients you would like more of.
Fill the super clean/hot jars (straight out of the dishwasher or 5 minutes in a 200 °F/100 °C oven) with the cherry tomato sauce.
Let sit for a couple of minutes, then fill the jars with olive oil, almost to the brim.
Close the jar with new, clean lids.