In a small bowl, whisk together mayonnaise, honey mustard and Dijon (if using) until smooth and uniform. Taste and adjust honey mustard or mayo to preferred balance. Set aside.

Prep apple slices

Thinly core and slice half an apple into 1/8" (3 mm) slices. Place slices in a small bowl and toss immediately with the 1/2 tsp lemon juice to prevent browning. Sprinkle the salted and pepper over the apples and toss gently to coat. Set aside.

Toast & Assemble Sandwiches

Toast bagels (optional)

Slice the bagels in half horizontally. Heat a skillet over medium heat and add the butter. When butter is melted and foamy, place cut bagel halves cut-side down and toast 1–2 minutes until golden and crisp. Alternatively, use a toaster or toaster oven. Remove and place cut-sides up.

Spread bagels

Evenly divide the prepared mayo–honey mustard spread and spread on both cut sides of each toasted bagel (about 1½ tbs per bagel half).

Layer cheeses and turkey

On the bottom half of each bagel, place two slices of cheddar followed by two slices of Swiss (or overlap as desired). Top the cheese with 4 slices of roasted turkey per sandwich, arranging to cover evenly.

Add onion, apple and arugula

Distribute the thinly sliced red onion evenly over the turkey (about 2 tbs / 1/4 cup per sandwich). Arrange the lemon-tossed apple slices in a single layer on top of the onion. Finish with about 1/2 cup arugula per sandwich (divide the 1 cup between two sandwiches).

Season and finish

Lightly season the assembled fillings with a small pinch of salt and a crack of black pepper. Place the top bagel half over the fillings, press gently to compact, and slice the sandwich in half if desired.

Serve

Serve the Kibbler immediately while bagel is still slightly warm and crisp. If making ahead, keep components separate (spread, apple, arugula) and assemble within 30 minutes of serving to retain texture.