To make the chicken schnitzel: Using a sharp knife, butterfly the chicken breasts. If you are unfamiliar with this technique, you'll want to cut it almost all the way in half through the middle leaving you with a larger, much thinner steak (see notes in the blog post). Pat the chicken dry with paper towels and season lightly with salt and pepper.
In a medium bowl, whisk together the flour, eggs, dijon, Worcestershire, water, 1 teaspoon of kosher salt, and 1/2 teaspoon of freshly ground pepper until smooth. In a separate, shallow dish or pie plate, combine the panko with the sesame seeds and za'atar until well-mixed.
Heat about 1 1/2 inches of canola oil in a wide-bottomed, high-sided pot (reduces splatter, a dutch oven works well, or a large cast-iron skillet) to 350 degrees F.
Dip the chicken into the batter and coat it well. Shake off any excess as you lift it from the bowl and then transfer it to the panko crumbs and coat it really well. Repeat with the second chicken breast.
One a time, gently ease the chicken into the oil and fry for 3-4 minutes per side, until deeply golden brown. Transfer to a wire rack set over a baking sheet and into a 200-degree F oven. This keeps the chicken warm and crispy while you fry the second piece.
To make the brussels sprout salad: heat a large skillet or cast-iron skillet over medium-high heat. Add the bacon fat and when the fat starts to shimmer, add the shaved brussels sprouts to the pan. Cook for about 2 minutes, stirring frequently until the sprouts are lightly charred. Transfer to a bowl and toss with the remaining ingredients. Season to taste with salt and pepper.
Serve immediately with lots of lemon wedges for squeezing.