In a large bowl, whisk together the mustard, yogurt and hot sauce. Add the chicken, turning to coat, and let stand at room temperature for 30 minutes (or cover and refrigerate for up to 12 hours).
Position a rack in the upper third of the oven and preheat to 400 degrees . Line a baking sheet with parchment and grease with 2 tablespoons olive oil.
In a large bowl, toss together the panko, italian seasoning, 1 teaspoon salt and 1/4 teaspoon pepper. Working with 1 chicken piece at a time, coat in the panko mixture and transfer to the prepared baking sheet. Drizzle with the remaining 2 tablespoons olive oil, then bake until golden and cooked through, about 40 minutes. Serve with the carrot sticks.