If making the roasted cherry tomatoes, preheat the oven to 340°F (170°C). Halve the cherry tomatoes and toss on a parchment-lined baking sheet with olive oil, balsamic vinegar, salt, and pepper. Roast for about 20 minutes.
Heat the olive oil in a large, deep pot over medium heat. Add the minced garlic and cook for about 30 seconds until fragrant.
Stir in the tomato paste and cook for about a minute until it darkens slightly.
Pour in the passata and broth. Add the balsamic vinegar, chopped basil stems, salt, pepper, and red pepper flakes if using. Bring to a simmer.
Add the pasta directly to the pot, mostly submerged in the liquid. Cover and simmer for about 10 minutes, stirring every couple of minutes to prevent sticking.
Once the pasta is nearly al dente, stir in the heavy cream. Add the shrimp and cook uncovered for 4-5 minutes, until the shrimp are pink and opaque and the pasta is fully cooked.
Remove from heat, stir in the chopped basil leaves. Top with roasted cherry tomatoes if using, and serve with toasted baguette.