For the vinaigrette: Heat the oil and garlic cloves in a small saucepan over medium-high heat until simmering. Adjust the heat to maintain a slow simmer. Cook until the garlic is tender and golden, 25 to 30 minutes. Let cool to room temperature. (The garlic and oil can be refrigerated in an airtight container for up to 1 month.)
In a food processor, combine the fried garlic, 1/4 cup of the garlic oil, the vinegar, 1 teaspoon salt and 1/2 teaspoon pepper. Puree until smooth.
For the salad: Combine the arugula, farro, cranberries and goat cheese in a large bowl. Toss with the vinaigrette.