Bring the vinegar, shallots, bay leaf, and thyme in a small pot over medium heat. Cook until reduced to a syrup, about 10 minutes. Remove the bay leaf and thyme, transfer to a small mixing bowl and cool to room temperature.
Wrap the base of the mixing bowl with a kitchen towel circle to keep the bowl from wobbling. Whisk in the honey, mustard and salt. Slowly drizzle in the olive oil, whisking constantly to emulsify. If the vinaigrette seems too thick, whisk in a teaspoon of cold water.
Put the arugula in a serving bowl and toss with some of the vinaigrette. Use a vegetable peeler to shave the ricotta salata over the arugula. (Extra vinaigrette will keep in the refrigerator, covered, for 3 days.) Toss to combine and serve.