With the rack in the middle position, preheat the oven to 180 °C (350 °F).
Dust the tenderloins with flour. In an ovenproof skillet, brown the meat in the butter and oil.
Season with salt and pepper. Remove from the skillet. Set aside.
Add a little butter in the skillet, if necessary, and soften the shallots.
Add the mustard and maple syrup and simmer for about 1 minute, until it thickens. Return the pork to the skillet and coat with the sauce.
Bake for 16 to 17 minutes for medium rare doneness.
Remove from the oven and cover with aluminum foil. Let rest for 5 minutes before slicing. Garnish with fresh thyme.
Serve with barley pilaf with bacon and/or mashed acorn squash with maple syrup.