Preheat the oven to 375°F. Coat a 9×13-inch glass or ceramic casserole dish with nonstick cooking spray.
Stir together the Dijon mustard, maple syrup, olive oil, and soy sauce in a small bowl. Add the minced garlic and chopped rosemary.
Arrange the chicken thighs in the prepared dish in one layer, keeping them close but not overlapping.
Pour the sauce over the chicken and spread it with a spoon until every thigh is coated.
Bake for 45–50 minutes. For unusually small thighs, begin checking at about 35 minutes. Cook until an instant-read thermometer registers at least 165°F in the thickest part and the surrounding liquid is simmering.
Spoon the pan juices over the chicken. Switch the oven to broil and broil for about 5 minutes, watching continuously, until the tops are golden brown.
Confirm a minimum internal temperature of 165°F and serve hot with the pan juices.