Make the chipotle sauce by combining 1 can chipotle chile (use 1 chile and 1 tsp adobo), 1/2 cup mayonnaise, 1/3 cup plain Greek yogurt, 1/4 cup chopped cilantro, 1/4 tsp ground cumin, 1/4 tsp dried dill and kosher salt to taste in a blender or food processor; puree until smooth, about 2–3 minutes. Refrigerate until ready to use.
Caramelize the onion: heat a small skillet over medium, add 1 tablespoon butter and the sliced 1/2 medium onion, and cook gently, stirring occasionally, about 15 minutes until soft and caramelized. Remove from pan and set aside.
Cook the chicken cutlet: heat a heavy-duty skillet over medium-high with 1 teaspoon oil. Season the chicken cutlet with salt and pepper and cook 2–3 minutes per side until golden.
Add 1/4 cup water to the pan, reduce heat to low, cover or simmer gently for 5 minutes until cooked through. Transfer to a bowl and let cool slightly, then shred the chicken with two forks or by hand to make about 1 cup shredded chicken.
Assemble sandwiches: butter one side of each bread slice with the remaining butter. On the unbuttered side of two slices, place an even layer of Gruyere, then divide the shredded chicken and caramelized onions between the sandwiches. Drizzle about 2 teaspoons chipotle sauce over each, top with more cheese and the remaining bread slices, buttered side out.
Grill the sandwiches: heat a griddle or skillet over medium, add a little butter if needed, and cook each sandwich 2–3 minutes per side until the bread is golden and the cheese is melted. Serve warm.
