Herb and Mustard Turkey with Green Onion Gravy

For herb and mustard butter:

Whisk all ingredients in medium bowl. DO AHEAD: Can be made 2 days ahead. Cover and chill. Bring to room temperature before using.

For turkey:

Set rack at lowest position in oven and preheat to 325°F. Sprinkle main turkey cavity with salt and pepper and spread with 2 tablespoons herb-mustard butter. Starting at neck end of turkey, carefully slide hand between skin and meat of breast, thighs, and upper drumsticks to loosen skin. Spread herb butter over thigh and drumsticks, then over breast meat under skin. Fill main cavity with parsley, sage, and thyme sprigs. Tie legs together loosely. Tuck wing tips under.

Place turkey on rack set in large roasting pan. Rub outside of turkey all over with oil; sprinkle with salt and pepper. Pour stock into pan. Roast turkey until thermometer inserted into thickest part of thigh registers 165°F to 170°F, about 3 hours. Tilt turkey so juices from main cavity run into pan. Transfer turkey to platter. Tent very loosely with foil; let rest at least 30 minutes (internal temperature will rise 5 to 10 degrees). Reserve pan.

For gravy:

Scrape juices and browned bits from reserved roasting pan into large glass measuring cup. Spoon off fat, reserving 2 tablespoons. Add enough stock to pan juices to measure 2 cups. Whisk together 2 tablespoons water and cornstarch in small bowl until smooth.

Heat 2 tablespoons reserved fat in large saucepan over medium heat. Add white parts of green onions. Sauté until beginning to color, about 6 minutes. Add degreased pan juices, 2 cups stock, and cream. Whisk in cornstarch mixture. Simmer until reduced to desired consistency, whisking occasionally, about 8 minutes. Stir in herbs and green onion tops. Season with salt and pepper.