In a 5- to 6-quart pan over high heat, bring 4 quarts water to a boil; add beans and cook just until barely tender to bite, about 1 minute. With a skimmer or slotted spoon, remove from water and transfer to a colander; rinse under cold running water until cool.
Bring water back to a boil. Add farfalle and cook until tender to bite, 14 to 16 minutes. Drain.
In a large bowl, mix pasta, beans, and 3/4 cup pesto. If more sauce is desired, add up to 1/4 cup more pesto. Top with cheese and halved cherry tomatoes.