Preheat oven to 450°. Toss potatoes and carrots in bottom of large baking 
dish with 1 tablespoon oil.Season with salt and pepper. 

Pat chicken dry with paper towels, drizzle with remaining tablespoon oil, 
and season with salt and pepper. Arrange, skin-side up, on top of 
vegetables in baking dish.

In a small bowl, stir together mustards, maple syrup, thyme, and 
red pepper flakes. Brush on top of chicken and drizzle any extra over 
vegetables. Roast chicken until golden and a thermometer inserted into
thickest part of thigh registers 160°, about 35 minutes. 
Remove from oven and brush thighs with chicken drippings. 
Turn oven to broil and broil thighs until deeply golden, 2 to 3 minutes.
Let cool slightly, then sprinkle with parsley before serving.