In a 10- to 12-inch oven-safe skillet (like cast iron), melt butter over medium heat and sprinkle flour over top and stir until combined and smelling nutty. Slowly whisk in broth and fairlife ultra-filtered milk. Simmer, stirring, until slightly thickened, about 3 minutes.
Add onion (if using) and cook 3 minutes. Stir in frozen veggies and cook until just warmed, about 3 minutes.
Stir in rotisserie chicken, thyme, salt, and plenty of black pepper. Taste and adjust seasoning.
Remove skillet from heat. Lay puff pastry sheet over the filling, stretching slightly if needed (it doesn't have to cover perfectly). Cut a few steam vents in the pastry. Brush with egg wash if using.
Transfer skillet to a 400°F oven. Bake until pastry is golden and filling is bubbling at the edges, about 25 minutes.
Let rest 10 minutes before scooping into bowls.
