Here's my recipe for an easy Italian pasta sauce using canned tomato sauce as your base. When I need a red sauce but don't have cans of crushed tomatoes, I use this instead! Makes about 6-8 cups.
Heat olive oil in pot over medium heat
Add in diced onion and cook until translucent making sure not to burn by stirring frequently (about 10 minutes)
Add in crushed garlic and keep stirring until very fragrant making sure not to burn the garlic at all! (about 2-3 minutes)
Add in the cans of tomato of sauce and stir
Take the diced tomatoes, put in a blender and pulse twice. This creates a crushed texture. You can also use a can of crushed tomatoes if you have one.
Add the tomato paste and stir until fully dissolved
Add the water, bay leaf and carrot and give a stir
Turn to a medium-low or simmer depending on time contraints. If you have a good chunk of hours then put it on simmer and let it simmer for 2-3 hours.
Stir occasionally over the next hour to make sure it doesn't burn or stick to the bottom of the pot
Give a taste test and if it's evaporated down too much for your liking, add a little more water and continue cooking. Since I'm using this for a lasagna, I don't want it thin in consistency. Add more tomato paste if it is too thin.
Remove and toss carrot when done. The carrot absorbs extra acidity so we don't want to keep it in the sauce.