Heat 2 Tbs. of the olive oil in a 12-inch nonstick skillet over medium-high heat. Add the shallots, chiles, bay leaf, and 1/4 tsp. salt; cook, stirring often, until the shallots begin to color, 5 to 6 minutes. Add the farro and thyme and continue to cook, stirring, until the farro smells nutty and makes a crackling sound, about 3 minutes more. Add the vegetable broth and 2 cups water and bring to a boil. Reduce the heat to maintain a simmer, cover, and cook for 5 minutes. Stir in the lentils, cover, and cook undisturbed until the farro is tender but chewy, the lentils are tender but firm, and nearly all of the liquid is absorbed, 25 to 30 minutes. Remove the skillet from the heat and let the pilaf stand, covered, for at least 5 minutes.
While the pilaf is cooking, heat the remaining 2 Tbs. olive oil in a 12-inch skillet over medium-high heat. Add the onions and 1/2 tsp. salt and cook, stirring frequently, until limp and deeply browned in spots, about 10 minutes. Add the balsamic vinegar, toss quickly until the onions are evenly coated, and then reduce the heat to low, cover, and let the onions steam for about 5 minutes.
Meanwhile, in a medium bowl, combine the scallions, carrots, cilantro, rice vinegar, ginger, sugar, and 1/4 tsp. salt. Let sit for 5 minutes to let the flavors meld.
Stir the onions and about three-quarters of the carrot mixture into the pilaf. Season to taste with salt.
Drizzle a little olive oil over the pilaf, garnish with the remaining carrot mixture, and serve.