Cook the farro in a large saucepan of boiling water seasoned with 2 teaspoons salt and cook until done, or when the grains are plump with a slight resistance in the center, about 20-25 minutes. Scoop out and reserve 1 cup of the cooking water before draining.
In a 10-12" skillet or sauté pan, add the oil and butter over medium heat; stir in the shallot and cook until softened (but not browned). Add the garlic and chili and cook a few seconds.
Stir in the tomatoes, 1/2 teaspoon salt and 1/2 cup of the reserved cooking water and bring to a simmer. Cook for about 10 minutes, then add the cheese and beans, stirring to incorporate.
Add the farro to the mixture, stirring gently; add more water if it seems too thick – it should be a little saucy. Scatter the basil over the farro and taste for seasoning. Serve with additional cheese at the table.