In a medium saucepan over medium-high heat, bring farro, broth, bay leaf, and ½ tsp. salt to a boil. Reduce heat to medium-low, bring to a simmer, and cook, stirring occasionally, until farro is tender and no broth remains, about 30 minutes. Transfer to a large serving bowl and let cool.
Meanwhile, in a small saucepan over medium heat, heat olive oil. Cook shallots, stirring occasionally, until beginning to bubble, about 5 minutes. Reduce heat to medium-low and cook, stirring occasionally, until shallots are golden and crisp, 15 to 20 minutes. Using a slotted spoon, transfer shallots to a paper towel-lined plate; season with salt. Let shallot oil cool.
Transfer shallot oil to a medium bowl. Add vinegar, mustard, and honey and whisk to combine; season with salt and pepper.
Add shallots, apple, arugula, Parmesan, pecans, basil, and parsley to bowl with farro. Drizzle dressing over and toss to coat.
