Add the butter and olive oil to a medium pot over medium heat. Add the shallot, stir and cook for 2-3 minutes until it's starting to cook through. Add the garlic and cook for an additional minute.

Add the tomato paste and stir to cook off slightly. Add the tomatoes and 1 cup of chicken broth. Cover the pot and let it cook until the tomatoes are broken down and jammy, about 5-10 minutes.

Reduce the heat to low. Add the gnocchi, remaining cup of chicken broth, and heavy cream. Stir until combined, then cover the pot. Simmer until the gnocchi is cooked through, about 5 minutes, stirring occasionally. If the sauce is getting thick, add an extra splash of water until your desired consistency is achieved.

Once the gnocchi is soft and cooked through, turn off the heat and divide into bowls. Top with burrata, a drizzle of olive oil, fresh cracked black pepper, and toasted breadcrumbs. Enjoy immediately!