Add the tomatoes to a large rimmed baking sheet, then drizzle the 2 1/2 tablespoons of extra virgin olive oil out over the tomatoes. Stir them gently to coat.
Bake the oiled tomatoes at 400° for 25-30 minutes, just until some of the tomatoes have burst and begun to shrivel.
Remove the tomatoes from the oven, and set aside.
Add the remaining extra virgin olive oil to a large sauce pan, and heat over medium until the oil's hot. It will appear shimmery when ready.
Stir in the onions, cooking for roughly 3 minutes- just until they've begun to soften and turn in color.
Add the garlic, tomatoes (including all the juices in the pan), and herbs to the sauce pan. Stir to combine.
Reduce the heat to a low simmer (low heat), cover the pan almost completely just leaving a small gap with a lid, and let the mixture simmer very gently for at least 30 minutes, but up to an hour. Stir occasionally.
Remove the pot from heat, uncover, and let rest for 10-15 minutes.
Using an immersion blender, blend the sauce until smooth- you can leave it chunkier if desired. If too thick, add some vegetable or chicken broth to thin.
Serve over a bed of your favorite pasta with fresh herbs.