Make the chipotle mayo: combine 1/2 cup mayonnaise, 3 chipotle peppers in adobo and 1–2 teaspoons of adobo sauce in a food processor or blender and pulse until smooth.
Prepare the focaccia: slice the loaf into quarters and then slice each quarter horizontally to form sandwich tops and bottoms.
Spread chipotle mayo onto both the top and bottom pieces of each focaccia quarter.
Assemble sandwiches: layer sliced cooked chicken, sliced fresh mozzarella, sliced tomato, thinly sliced red onion, and chopped basil on the bottom halves, then place the top halves over them.
Heat and toast: lightly grease a panini press (or heat a skillet and brush with oil). Press each sandwich in the panini press for 4–5 minutes, or cook in the skillet, pressing with a spatula or weighted pan, until the cheese melts and the bread is crispy.
Serve immediately while hot.