In a wide pot, heat 1 tablespoon neutral cooking oil over medium heat. Add the shallot and garlic scapes and cook for 2 minutes or until fragrant.
Add the fennel wedges and cook for 5-6 minutes or until beginning to char around the edges.
Add 2 tablespoons butter. Once melted and frothy add the tomatoes. Cook, mashing a few of the tomatoes lightly until the tomatoes are softened and a thin sauce begins to form. Season with salt and pepper.
Add the shaved squash and toss to combine. Cook for 5 minutes until softened. Taste and season with salt and pepper.
Transfer the squash pappardelle to a serving platter. Wipe out the skillet.
Cook the Trout:
Heat 1 tablespoon oil in the pot over medium-high. Once hot and shimmering, add the trout fillets, skin-side down, and cook without moving for 3-4 minutes until the skin is very crispy. Flip and cook an additional 2-4 minutes or until the fish is cooked through. Turn off the heat and transfer to plate.
To Serve:
Divide the squash pappardelle between plates and serve with a trout fillet on top. Garnish with reserved fennel fronds and a sprinkle of flaky sea salt, if desired. Enjoy!