Pat the chicken leg dry. Season both sides with salt and pepper. Place between two layers of plastic wrap and pound gently until flattened to an even thickness.
Heat oil in a frying pan over medium-high heat. Fry the chicken leg for 5 min, then flip. Continue frying for 5 min until the internal temperature reaches 74°C (165°F). Set aside.
Heat a frying pan over medium heat. Place the burger bun halves cut-side down in the pan. Toast for 2 to 3 min until lightly golden and crispy.
Cut the cucumber into rounds. Slice the tomato into thin slices. Slice the red onion thinly.
Cut the red cabbage and carrots into thin strips. Season with a pinch of salt and pepper.
In a small bowl, mix together the mayonnaise and adjika until well combined.
Heat a small amount of oil in a frying pan over medium heat. Crack the egg into the pan and fry for 3 to 4 min until cooked to your preference.
Spread the mayonnaise-adjika sauce on the bottom bun. Layer with the cabbage-carrot slaw, cucumber slices, tomato slices, red onion, smoked sausage cheese, and the cooked chicken leg. Top with the fried egg and place the top bun on top.