Melt 2 tablespoons butter in a skillet over medium heat. Add onions and celery; cook and stir until golden brown, about 6 minutes. Remove from heat.
Place bread cubes, poultry seasoning, cooked onions and celery, salt, and pepper in a mixing bowl. Pour in chicken broth. Toss until thoroughly blended. Let mixture rest for about 15 minutes to allow broth to absorb into the stuffing. Add egg yolk; stir until evenly incorporated.
Preheat oven to 375 degrees F (190 degrees C). Line a rimmed baking sheet with parchment paper.
Slice turkey breast crosswise in 3/4-inch slices down to the bone (do not cut through the bone). Divide stuffing mixture among the spaces between the slices. Transfer turkey breast to prepared baking sheet. Brush with melted butter.
Roast in preheated oven until richly browned, 60 to 75 minutes. An instant-read thermometer inserted near the bone should read 150 degrees F (65 degrees C). Remove from oven and let rest 10 minutes before slicing sections from bone.