Heat oven to 300 degrees Fahrenheit.
Wash tomatoes and cut them in half. Squeeze each half gently over your sink or compost bin to remove excess juice and seeds.
Chop squeezed tomatoes into coarse pieces.
Heat olive oil in a deep skillet over medium heat, and add chopped tomatoes, salt, and any additional herbs or spices.
Bring tomatoes to a boil, then lower your heat and simmer for about 15 minutes, or until the tomatoes are soft.
Place simmered tomatoes into a blender and blend at high speed until fully pureed (including the skins and any seeds that didn't get squeeze out).
Rub a deep, rimmed baking sheet with a bit of olive oil and pour the tomato puree into it. Five pounds of tomatoes should just fit into a deep, 13" x 18" rimmed baking sheet.
Bake the puree slowly, using a spatula to turn and mix the puree periodically during cooking. As the water evaporates, you'll notice that the edges of the puree will start to darken; look for this darkening as a sign that it's time to mix the puree and spread it out evenly over the baking sheet again as it thickens.
It can take anywhere from 3 to 4 hours for tomato paste to cook fully (oven temperatures can vary). If you notice that the edges seem to be burning instead of browning, turn your oven down by 50 degrees. (NOTE: Using a smaller baking pan will result in a deeper layer of tomato with less surface area available for evaporation; your cooking time will increase significantly!)
When the tomato paste is thick and brick-colored, the tomato paste is done!
Store the tomato paste in the refrigerator for several weeks in a sealed container; cover your tomato paste with a layer of olive oil to increase its keeping qualities. You can also freeze tomato paste in individual small containers for six months (take out what you need and let thaw in the refrigerator).