Preheat the oven to 220°C, fan-forced. Bring a steamer pot of water to a boil for the potatoes. Line a large oven tray with baking paper. Cut the carrots and courgette into 1cm-thick batons. Slice the cheese.
PREP CHICKEN
Put the chicken flat on a board, put your hand on top and slice a pocket horizontally into each fillet. Fold the cheese slices in half and place inside each pocket. Do the same with the ham. Whisk the egg in a bowl. Combine flour and a pinch of salt in a shallow dish. Combine the breadcrumbs in a separate shallow dish. Dust the chicken with the flour, shake off the excess, then dip in the egg and coat in the breadcrumb mixture. Season with salt and pepper and spray with oil. (Tip: Use toothpicks to close and hold each pocket closed).
ROAST CHICKEN & CARROTS
Put the chicken and carrot on the lined tray. Drizzle the carrot with the first measure of oil, season with salt and pepper and toss to coat. Roast the chicken and carrot for 12 mins, or until the chicken is cooked through.
PREP & COOK POTATOES
Meanwhile, peel the potatoes and cut into 5cm chunks. Put the potatoes in the steamer pot of boiling water and cook for 12-15 mins until tender. Then drain the water and transfer the potato into the empty pot. Mash the potato until smooth. Add the second measure of oil, the first measure of milk and season with salt and pepper and stir until well combined.
MAKE SAUCE
Heat the third measure of oil over medium heat in a small pot. Add flour and cook for 1 minute. Add half the second measure of milk and whisk until the flour mixture is blended in. Gradually add the remaining milk and mustard and then grate in the cheese. Cook for 3 minutes, whisking constantly, until thickened. It will thicken as it cools.
TO SERVE
Divide the chicken cordon bleu with mash and roast veggies between plates. Drizzle over the Dijon cream sauce.