In a large, shallow bowl, mix together the breadcrumbs, almonds, garlic powder, onion powder, dried thyme, 1 teaspoon salt and ½ teaspoon pepper.
Add the flour to another shallow bowl, then in a third bowl whisk together the eggs and Dijon mustard until well combined.
Season each piece of chicken with salt and pepper on both sides.
Take a piece of chicken and dip it into the flour to coat on all sides, then tap off the excess. Next, coat it in the egg mixture, let the excess drip off, then place it into the breadcrumb mixture. Be sure to press it down and move it around so that it gets thoroughly coated. Repeat with the remaining pieces.
Place a cooling rack over top of a sheet pain and set it next to the stove for draining the cooked chicken.
Heat about ½ inch of oil in a large, heavy bottomed sauté pan over medium-high heat. Gently place 1-3 chicken breasts down in the hot oil, but don't overcrowd the pan. Cook until golden brown on each side, then remove to the cooking rack to drain. Repeat with the remaining chicken breasts, wiping out the pan and starting with new oil as needed.
While the chicken cooks, make the salad. Add the shaved Brussels sprouts, arugula and apples to a large bowl. In a separate small bowl or jar, whisk together the shallot, Dijon mustard, lemon juice, salt and pepper. Slowly whisk in the olive oil until emulsified, then pour over the salad and toss until everything is nicely coated.
Serve almond chicken cutlets hot with salad on the side.