Use a pot large enough to parboil 10 large tomatoes. (Ideally a 12-quart pot, but you can use a tall, 8-quart pot to parboil the tomatoes in two batches.) Fill the pot ⅔ full with hot water. Place it over high heat on the stove and cover it so it will come to a boil.
Rinse the tomatoes and use a small knife to cut out the cores. Prepare an ice bath by filling a large bowl with ice and water. Set the cored tomatoes and ice bath near the stove.
When the water is boiling, use a slotted spoon to add as many tomatoes as will fit into your pot. Let the water come to a boil again, and parboil the tomatoes uncovered, for three minutes or until their skins are loosened. Use the slotted spoon to transfer the blanched tomatoes to the ice bath. Parboil any remaining tomatoes if needed.
After the blanched tomatoes have rested in the ice bath for five minutes, it's time to peel them. Gently pull off the skin with your fingers and discard it. On a large cutting board, use a sharp knife to cut a tomato in half, then slice each half into wedges about 1 ½-inches thick. Scrape out the seeds from each wedge. (It helps to place the seeds in a fine-mesh strainer placed over a medium bowl to catch any tomato juice that can be used later.) Place the cleaned tomato wedges into a large mixing bowl.
Continue peeling, cutting and seeding the remaining tomatoes. Pour any extra tomato juice (from under the fine-mesh strainer of seeds) into the bowl of cleaned tomatoes. You also can use the back of a spoon to press the seeds down into the strainer to squeeze out any extra juice to use.
Pour ¾ cup of olive oil over the cleaned tomato wedges in your bowl. Peel the garlic cloves and thinly slice them. Add the garlic to the bowl of tomatoes and olive oil and stir to combine.
You can proceed to make the sauce within two hours or cover the bowl and refrigerate the tomatoes for up to a day before cooking the sauce. The tomatoes will become more flavorful as they sit in the garlic-infused oil. Let them come to room temperature before cooking them.
Make the fresh tomato sauce
Peel the onion and chop it until you have one cup of chopped onion.
Drain and dry the pot you used to parboil the tomatoes. Scoop out two or three tablespoons of oil from the bowl of tomatoes and add the oil to the pot. Heat on medium-high. Add the chopped onions and sauté them, stirring frequently, until they're soft, which should take around five minutes.
Pour the tomatoes, garlic and remaining olive oil into the pot with the onions. Stir in the salt, pepper and pepper flakes, noting the time. Heat on high, loosely covered with a spoon resting on the edge of the pot, until it comes to a boil. When the pot is boiling, lower the heat, uncover the pot and stir in the tomato paste. Simmer the sauce uncovered, for two hours past the time you first added the tomatoes. Stir occasionally to prevent sticking.
When the spaghetti sauce has cooked for at least two hours, rinse the sprigs of basil and pat them dry with a paper towel. Stir the basil into the pot. Turn off the heat and serve the sauce stirred into cooked pasta and ladled on top.
When the sauce is no longer hot, store leftovers in one or more sealed containers in the refrigerator. The sauce will keep in the refrigerator for up to five days. You also can freeze leftover tomato sauce for up to three months for best quality.
Notes
The sauce makes enough for 1.5 pounds of pasta.
The best tomatoes to use for fresh tomato sauce are big, soft, juicy ones from the garden. If you need to buy them, look for them at farmers markets or buy locally grown ones at the grocery store.