In a skillet over medium heat, drizzle in 3 tablespoons of the olive oil. When hot, add the garlic slices and sauté for a few minutes, being careful that they don’t burn. Add the peppers and salt. Turn the heat to medium-high and sauté until the peppers start to soften. Add the tomato paste and cook for 1 minute with the peppers.
In a large bowl, pour in the canned tomatoes. Use a fork or knife to slice the tomatoes, or use your hand to mash them. Pour them along with all juices into the skillet. Turn the heat to low and simmer until the tomatoes cook down, 10 to 15 minutes.
Turn off the heat. Tear pieces of fresh basil and add them to the pan. Drizzle with the remaining 2 tablespoons oil and taste for seasoning. Serve with meatballs or use as a sauce over pasta.