For the mustard sauce: Whisk together the honey, Dijon mustard, whole-grain mustard and horseradish in a small bowl and season with salt and pepper. Cover and let sit to allow the flavors to meld while you make the chicken.
For the chicken roulade: Preheat the oven to 400 degrees F.
Heat 2 tablespoons of the canola oil over low heat in a large saute pan. Add the garlic and red chile flakes and cook for 30 seconds. Increase the heat, stir in the baby arugula, season with salt and pepper and cook until just wilted, about 2 minutes. Set aside.
Drizzle the chicken breasts with a little oil and thinly pound between 2 sheets of parchment paper or plastic wrap. Put the breasts on a flat surface skin-side down, and sprinkle the top sides with salt and pepper. Place 2 slices of the ham on each breast; spread 2 ounces of the cheese over the ham and then top with one-quarter of the arugula in the center. Roll the breasts tightly and tie with butcher's twine. Sprinkle the roulade with salt and pepper.
Heat a large ovenproof saute pan over high heat. Add the remaining 2 tablespoons oil and cook until it begins to shimmer. Put the rolls in the pan seam-side up and add the butter. Cook until golden brown on all sides, about 3 minutes. Transfer the pan to the oven and continue cooking until the breasts are just cooked through and the cheese has melted, 4 to 5 minutes.
Remove the rolls to a plate and let rest 5 minutes before slicing. Serve with the mustard sauce and topped with a bit of micro arugula.