Preheat an oven. Heat olive oil and butter in a large skillet or braiser over medium-high heat. Add diced onion, diced carrots, and chopped celery. Season with Kosher salt, then cook, stirring occasionally, until softened. Add garlic cloves, then cook.
Add chopped sage, chopped rosemary, chopped thyme, sweet paprika, black pepper, and curry powder (optional) then stir and cook.
Add all-purpose flour to the pan, then cook for 1 minute, stirring the whole time. The flour should absorb any liquid in the skillet.
Slowly whisk in chicken broth, being sure to scrape any browned bits off the bottom of the pan. Stir in heavy cream, then whisk well. Bring the mixture to a simmer until just barely bubbling, then add the pulled rotisserie chicken, parboiled potatoes, and frozen peas.
You can cut the puff pastry into a circle to match the size of the pan. Instead, we like to either make a lattice topping or cut the puff pastry into smaller 2×2-inch squares, then overlap them to cover the entire top of the skillet.
In a small bowl, whisk together large egg and heavy cream or milk. Brush this on top of all exposed puff pastry. Sprinkle grated Parmesan on top along with a little freshly ground black pepper, and a generous pinch or two of flaky sea salt.
Transfer to the oven and bake until the puff pastry is golden brown and crispy.