Make the Dijon Mustard Vinaigrette: Put the shallots, vinegar, bay leaf, and thyme into a small pot set over medium heat. Cook the vinegar until it is reduced to a syrup, about 10 minutes. Remove the bay leaf and thyme stem.
Pour the reduction into a mixing bowl. Set the mixing bowl on a kitchen towel shaped into a circle to prevent the bowl from wobbling. Whisk in the honey, mustard, and salt. Slowly drizzle in the oil, whisking constantly to emulsify the vinaigrette. If the vinaigrette appears to thicken too much, add a teaspoon of cold water.
Put the arugula in a bowl and dress with the Dijon Mustard Vinaigrette. Use a vegetable peeler to shave the ricotta salata into the arugula. Toss to combine.