Preheat your oven to 425 degrees Fahrenheit.
Cut the larger tomatoes into thick wedges and halve the cherry tomatoes, leaving the smallest ones whole. Do not peel or seed anything, since the skins soften completely and the seeds disappear under the blender.
Fill the 8x8 dish with the tomatoes, packing them in snugly and slightly mounded, because everything collapses as it roasts.
Tuck the onion wedges and whole garlic cloves in among the tomatoes, then scatter the basil leaves and chopped parsley over the top.
Drizzle the olive oil evenly over everything and sprinkle with the dried oregano. Dried herbs go in before roasting because they hold up to high heat and bloom in the oil.
Roast for 35 minutes, until the tomatoes have collapsed, the skins have split and pulled back, and the onion edges have darkened. Those browned edges are where the savory depth comes from, so let them happen.
Scrape the entire contents of the pan into a half gallon jar, juices and all. That liquid has already reduced in the oven, which is what makes this soup thick without any thickener.
Blend with an immersion blender for 30 seconds to a minute, until smooth and velvety. Blend less if you want a rustic soup with visible texture.
Stir in the balsamic vinegar, sugar, salt and black pepper. Taste and adjust, since tomato acidity swings widely depending on variety and ripeness.
Stir in the half and half off the heat. Start with the full quarter cup, then taste and add more if you want a milder, rounder soup.
Pour the heavy whipping cream into a zip top bag, twist the bag so the cream gathers into a small ball in one corner, and shake it back and forth for about a minute until it thickens into a light whip.
Snip a small corner off the bag and drizzle the whipped cream over the soup in a spiral. Drag a toothpick through it from the center outward to feather the pattern, or leave the spiral as it is.
Serve warm with thick sliced sourdough for dipping.