In a medium bowl, whisk together the vinegar and mustard. Slowly whisk in 1/2 cup of the oil. Stir in the shallot and thyme and season with salt and pepper to taste. Put the arugula in a large bowl. Core the pear and cut it into matchsticks.

Put the flour in a pie pan or large plate. Season the pork liberally with salt and pepper and dredge in the flour. Set a heavy 12-inch skillet over medium-high heat. Add the remaining 3 tablespoons oil and the butter. When the butter melts and begins to lightly brown, cook the pork (in batches if necessary), flipping after 2 min., until it's just cooked through, about 3 min. total. Transfer to a large plate. Repeat with the remaining pork.

Discard any fat in the skillet and set over low heat. Add the balsamic-Dijon vinaigrette and cook, stirring to pick up any browned bits on the bottom of the pan, until the sauce is warm, about 1 min. Pour the vinaigrette back into its bowl and whisk to recombine. Toss the arugula with half of the warm vinaigrette. Arrange the arugula on 4 plates. Top with the pork, pear, blue cheese, and dried cherries, and drizzle with the remaining vinaigrette.