Heat oven to 350° F. Line rimmed baking pan with parchment paper.
In large bowl, whisk egg; gently mix in turkey, onion, oat milk, breadcrumbs, pumpkin pie spice and 1/2 teaspoon salt. Form turkey mixture into eight (4-by-2 1/2-inch) loaves; place on prepared pan. Bake loaves 40 minutes, or until internal temperature reaches 165° F.
In large skillet over medium-high heat, heat oil; add mushrooms and cook 5 minutes, or until tender, stirring occasionally. In medium bowl, whisk chicken stock and flour; add to skillet and cook 3 minutes, or until thickened, whisking occasionally. Whisk in yogurt, pepper and remaining salt.
Serve loaves topped with gravy and sprinkled with parsley.