Cook farfalle in water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Meanwhile, season chicken with its salt and pepper. Heat 1 tablespoon oil in a large skillet and cook chicken for 7 to 8 minutes until browned and at least 165°F; transfer to a plate.
Reduce heat to medium-low and add remaining oil and garlic. Cook for 2 to 3 minutes until pale golden, then add broth and peas and simmer for 2 minutes.
Return chicken and add farfalle with 1/2 cup reserved pasta water. Toss for 1 to 2 minutes until the pasta is tender and the peas are hot.
Remove from heat and stir in Parmesan gradually, adding more pasta water if needed for a smooth light coating. Serve immediately.