In a small bowl, combine 1/2 cup mayonnaise, 1 1/2 tablespoons prepared horseradish, 1 teaspoon fresh lemon juice, 1/4 teaspoon kosher salt and 1/8 teaspoon black pepper. Whisk until smooth and taste; adjust horseradish for more heat (add in 1/2 teaspoon increments). Chill while preparing other components to let flavors meld.

Optional - toast challah

If desired, lightly butter one side of each challah slice with the tablespoon of butter. Heat a skillet over medium heat until warm, then toast slices butter-side down until lightly golden, 45–60 seconds. Alternatively, use a toaster or leave bread untoasted.

Filling

Prepare avocado

Halve and pit the avocados. Scoop flesh into a bowl and slice or mash to desired texture. Drizzle with 1 teaspoon olive oil, season with 1/4 teaspoon salt and 1/8 teaspoon black pepper, and toss lightly to coat. This prevents browning and seasons the avocado.

Slice tomato and onion

Cut the tomato into 6–8 thin slices. Slice the red onion very thinly (use 2–3 thin rings per sandwich). If onion is strong, soak slices in cold water for 5 minutes and drain.

Assemble sandwiches

Lay out 4 bottom slices of challah. Spread about 1 tablespoon of horseradish aioli evenly on each bottom slice. Layer 4 ounces (about 4 oz) of roasted turkey breast on top of the aioli. Add 2 slices of Swiss cheese over the turkey. Fan or spread about 1/2 of a prepared avocado (sliced or mashed) over the cheese. Top with 1–2 leaves of lettuce, 2 tomato slices, and a few thin red onion rings. Spread another 1 tablespoon of aioli on each top slice of challah and place top slice aioli-side down to finish each sandwich.

Optional - press or grill

If you prefer the cheese melted, place assembled sandwiches in a preheated panini press or skillet with a weight on top and heat over medium-low until cheese softens, about 2–4 minutes per side if using a skillet with a cover. Remove and let rest 1 minute before cutting.

Serve

Cut each sandwich in half on the diagonal. Serve immediately with pickle spears or chips on the side.