Heat a large sauté pan to medium heat. Add the olive oil and shallot and cook for 2-3 minutes. Add the baby broccoli and cook for 5 minutes, stirring occasionally. Add the garlic and cook for 1 more minute.
Add the can of San Marzano tomatoes to a blender and blend until smooth, just a few seconds. Add to the pan, then add the basil and salt. Stir occasionally and cook for another 5 minutes.
Preheat the oven to 375° F.
Separately (this can be done while preparing the sauce), bring a pot of water to a boil and add the quick-cook farro. Cook for 12 minutes or according to the package instructions. Drain, reserving 1 cup of the cooking liquid.
Add the farro, 1 cup cooking liquid, and cannellini beans to the tomato sauce and stir to combine.
Top with ½ cup grated parmesan cheese and the burrata broken up into pieces and placed in dollops on top of the farro dish. Bake for 8-10 minutes to heat through and melt the cheese. Serve with additional parmesan cheese.