Heat the olive oil in a large saucepan over medium heat until it shimmers and starts to emit a gentle aroma.
Add the minced garlic to the hot oil, stirring quickly until fragrant, about 30 seconds. You should hear a soft sizzle and smell the aroma of garlic filling the kitchen.
Pour in the chopped ripe tomatoes, and stir to coat them evenly with the garlic and oil. Let the mixture come to a gentle simmer, with bubbling around the edges, as the tomatoes begin to break down.
Add the dried chili flakes for a hint of heat, stirring into the simmering tomatoes. Keep stirring occasionally as the tomatoes soften further and release their juices.
Allow the sauce to simmer gently for about 20-25 minutes, stirring every now and then. You'll notice the mixture thickening and the tomatoes becoming glossy and smooth, with some chunks remaining for texture.
Stir in the balsamic vinegar, which will deepen the flavor and add a subtle sweetness. Taste and adjust with salt and black pepper to your liking.
Continue to simmer the sauce uncovered for another 5-10 minutes, allowing it to thicken further and develop a shiny, fragrant appearance. The sauce should coat the back of a spoon smoothly.
Remove the sauce from heat and let it rest for a few minutes. The final texture should be rich, slightly chunky, glossy, and bursting with the aromas of garlic and slow-cooked tomatoes.
Serve the warm tomato sauce over cooked pasta, roasted vegetables, or use as a base for other dishes. Enjoy the deep, layered flavors with each spoonful.