Select a large stockpot and fill with enough water to cover the tomatoes. Set the water to boil. Place the tomatoes in the pot of boiling water for 2 minutes, no longer. Drain the tomatoes in a colander and cool quickly by running cold water over them. Let cool briefly; cut an X in the bottom of the tomato with a knife. Peel the Roma tomatoes and chop them, keeping the liquid as well.
Pulse the red onion and garlic in the food processor until finely diced, scraping the side of the container. Set aside.
In a food processor, combine the Roma tomatoes with the canned tomatoes, including the liquid. Pulse for a few moments until semi-smooth yet still chunky. Place in a medium bowl.
Heat the large stockpot on medium heat for 3 minutes. Add olive oil. When shimmering, add red onion, garlic, carrot, black pepper, red pepper flakes, and 1 teaspoon sea salt. Saute for 10 minutes, until the vegetables are soft, stirring occasionally with a wooden spoon. Set heat to medium-low to avoid burning the vegetables.
Add the tomato paste and reserved tomatoes, stir to combine, and bring to a boil on medium heat. Reduce heat to medium-low, adding remaining salt, and simmer, uncovered, for 45 minutes, stirring occasionally. Taste for seasoning. Add more salt and pepper if desired. The sauce will have cooked down. Remove from heat, stir in baking soda until it dissolves, and stir in the basil.
Notes
Refrigerate the remaining sauce after it has cooled for up to 3 to 4 days, or freeze it for up to 4 to 6 months.
This recipe can be doubled or tripled and stored in the refrigerator or freezer.
Adjust seasonings to your taste! If you like spice, add more red pepper flakes.