Cut the carrot into 1/4-inch (about 5 mm) sticks. Place in a microwave-safe dish, cover with plastic wrap, and microwave until just tender, about 1 minute at 600W.

Slice the chicken breast horizontally into 4 thin pieces. Alternatively, pound the chicken to flatten it if you prefer.

Lightly season the chicken with salt and pepper. Place green beans and carrot sticks on each piece of chicken and roll them up. Secure the ends with toothpicks.

Sprinkle the chicken rolls with all-purpose flour using a fine sieve. You can skip this step, but the sauce will stick better if you do it.

Heat a frying pan over medium heat and add the vegetable oil. Place the chicken rolls seam-side down in the pan. Cover and cook over medium heat for about 10 minutes, turning occasionally, until cooked through.

Add the sauce ingredients to the pan. Simmer until the sauce thickens. Cover and let the rolls finish cooking in the residual heat. This also keeps them warm until serving.

Remove the toothpicks, slice the rolls into bite-sized pieces, and enjoy!