Step 1: Make the Potato Dough
Boil the peeled and cubed potatoes in salted water until very tender (about 15 minutes). Drain thoroughly.
While the potatoes are still hot, mash them until completely smooth (a ricer is perfect for this). Let them cool for 5-10 minutes.
In a large bowl, combine the warm mashed potatoes, butter, warm milk, and one egg. Mix until well combined.
Gradually add the 1 ¼ cups of flour, salt, and garlic powder. Mix until a soft, slightly sticky dough forms. It will be softer than traditional bread dough.
Turn the dough out onto a well-floured surface and knead gently for 2-3 minutes, adding just enough flour to prevent sticking. Form into a ball, cover with a towel, and let it rest while you make the filling.
Step 2: Make the Chicken Filling
Heat olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and pepper and cook until golden brown and cooked through. Remove from the skillet and set aside.
In the same skillet, add the onion and mushrooms. Cook until softened and the mushrooms have released their liquid, about 6-8 minutes. Add the garlic and cook for one more minute.
Sprinkle the 3 tablespoons of flour over the vegetables and cook, stirring, for 1 minute to cook out the raw flour taste.
Gradually whisk in the chicken broth, scraping up any browned bits from the bottom of the pan. Then, stir in the heavy cream and thyme.
Bring to a simmer until the sauce thickens. Stir the cooked chicken (and frozen peas, if using) back into the skillet. Taste and adjust seasoning. Let the filling cool slightly.
Step 3: Assemble the Roll
Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
On a well-floured surface, roll the potato dough out into a large rectangle, about 12×15 inches and ¼-inch thick. If the dough is sticky, keep the surface and rolling pin floured.
Spread the cooled chicken filling evenly over the dough, leaving a 1-inch border around all edges.
Starting from one long side, carefully and tightly roll the dough over the filling, using the parchment paper to help you lift and roll, just like a jelly roll. Finish with the seam side down.
Carefully transfer the roll, seam-side down, to the prepared baking sheet. Tuck the ends under slightly.
Brush the entire surface with the beaten egg wash and sprinkle with sesame seeds or everything bagel seasoning.
Step 4: Bake and Serve
Bake for 35-45 minutes, or until the crust is a deep, golden brown and firm to the touch.
Crucial Step: Let the roll rest for 15-20 minutes before slicing. This allows the filling to set, preventing it from spilling out.
Use a sharp serrated knife to slice into thick portions and serve.