Combine chicken broth and water in a large saucepan and heat on medium-low for 3-5 minutes.

Heat olive oil in a Dutch oven or large deep skillet over medium heat.

Add onions, carrots, and celery to the skillet.

Cook, stirring frequently, until softened (3-5 minutes).

Add farro to the vegetable mixture and cook, stirring, for 1 minute.

Stir in white wine and cook for 2 minutes, stirring occasionally.

Add 1 cup of the broth mixture to the farro.

Cook for 5 minutes, stirring frequently, until most of the broth is absorbed.

Repeat with remaining broth in 1-cup batches, cooking the final batch until the farro is tender.

Add frozen peas, parsley, and pesto.

Cook for 2-3 minutes, stirring frequently, until heated through.