Preheat oven to 400 degrees Fahrenheit.
In a large, wide cast iron skillet, heat the olive oil over medium-low heat. Add onions and leeks and begin to cook, stirring occasionally, until they become softened and slightly translucent, about 5 to 7 minutes. Season well with a couple generous pinches of kosher salt and a pinch of ground black pepper.
Add the red cabbage and begin to cook it down, another 5 minutes. Add garlic and the herbs de Provence. Cook the vegetables, stirring occasionally, until the cabbage is soft with edges that begin to brown and caramelize. The process will take approximately 40 minutes. The veggies will smell slightly sweet and fragrant.
Lay pastry sheet on a rimmed parchment-lined baking sheet. Flour a rolling pin and roll out the puff pastry gently until it measures about 18 x 13 inches. Spread the cabbage and onion mixture over the pastry, leaving a generous 1-inch border. Fold over the border and crimp at the corners.
Create egg wash by whisking together egg and water. Brush the edges of the puff pastry with egg wash. Sprinkle a mix of flaked sea salt and more herbs de provence.
Bake for 30 to 40 minutes, until the pastry is nicely browned along the edges. Cool tart for 5 minutes, then sprinkle the chopped scallions and parsley on top. Cut into slices and serve.