Toast bagel cut faces under the broiler for 1 to 2 minutes until lightly golden, then set aside. Stir Dijon and honey together and spread over the four top halves.
Heat a large skillet over medium heat. Sear ham in two batches for 2 to 3 minutes per side until lightly browned and heated through to 165°F, then transfer to a plate.
Melt butter in the skillet, add pear slices and pepper and cook for 3 to 4 minutes, turning gently, until just softened with a few browned edges.
Put one warm ham slice on each bagel bottom, divide pear slices evenly over the ham and cover with Swiss. Set the filled bottoms on a sheet pan.
Broil for 1 to 2 minutes until the cheese melts, watching so the bagel edges don’t scorch. Close with the mustard-spread tops and rest for 1 minute before cutting.