Begin by preparing the farro. Place the farro and chicken broth in a medium saucepan and add enough water to cover the farro by approximately 1-1/2 inches. Bring the mixture to a boil for 1 minute, stir, then reduce the heat to a moderate simmer.
Cook for 15 minutes, stirring occasionally. Test for doneness and season to taste, then continue cooking until the farro is cooked to your liking, 5 to 15 minutes longer. Drain any liquid that hasn't been absorbed.
Whisk the olive oil together with the balsamic vinegar and Dijon-style mustard. Drizzle over the cooked farro, combine well and set aside.
While the farro cooks, trim any white tendons from the chicken tenderloins, season on both sides with salt and pepper and set aside.
Add 2 tablespoons of olive oil to a large frying pan and heat over medium-high heat. Add the chicken in a single layer and cook until the tenderloins are barely golden and cooked through, 1-1/2 to 2 minutes per side. Transfer to a plate and set aside.
Add a bit more olive oil to the pan and reduce the heat to medium. Add the onion and sauté until soft and translucent, 4 to 5 minutes. Add the garlic and continue cooking until fragrant, 1 to 1-1/2 minutes longer.
Add the cherry tomatoes and combine well. Continue cooking, stirring often, until the cherry tomatoes are softened, 2 to 3 minutes. Taste and adjust the seasoning as needed and remove from the heat.
To assemble the bowls, divide the farro between 4 serving bowls, add 3 chicken tenderloins to each along with a portion of the tomato-onion mixture. Top each bowl with basil, fresh mozzarella and toasted pine nuts. Serve immediately.