Melt butter in small saucepan and whisk in flour. Cook down the flour (3-5 mins) until smooth and golden. Slowly add the milk and continue whisking. Let it simmer for about 10 minutes as it starts to thicken. Sprinkle in cheese and stir until melted. Season appropriately.
In a medium sized mixing bowl, combine the chicken, cheese sauce, and pesto. To me, the mayo-hater, it resembles chicken salad. Assemble the sandwiches: chicken mixture, spinach, and then a slice of Swiss cheese on each divided section of the baguette. Heat and oil your panini press and grill until browned and oozing with cheese. Serve immediately.