Preheat the oven to 425 degrees(F).
Spread the tomatoes and garlic out evenly on a large sheet pan. Drizzle with one tablespoon of olive oil and sprinkle with a few pinches of salt and pepper. Toss to coat the tomatoes evenly.
Roast for 25-30 minutes or until the tomatoes have burst and are starting to brown.
Once the tomatoes are done, add the tomatoes and garlic to a blender with 1 cup of vegetable broth. Puree until completely smooth. Set aside.
Heat the remaining tablespoon of olive oil on medium in a large pot. Add the Calabrian chilies and shallots to the pot. Sauté, reducing heat as needed, until the shallot is translucent. About 2-3 minutes.
Pour the roasted tomato puree you made into the pot, as well as the rest of the remaining 3 cups of broth and the vegan cream. Stir to combine.
Bring to a simmer, then reduce heat to medium low and let simmer for 5 to 10 minutes, allowing it to thicken a bit.
Add the basil, oregano and a pinch of salt and pepper. Stir to combine. Taste and adjust seasonings.
Serve a bowl with a drizzle of the olive oil on top with vegan grilled cheese that has been brushed with the olive oil.