Preheat oven to 200°C / 400°F. Line a baking sheet with parchment paper.
Bring a large pot of salted water to a boil. Add pasta and cook until a few minutes before al dente. Drain water, reserving a cup of pasta water. Set aside.
Place salmon fillet on prepared baking tray. Season with salt and black pepper. Drizzle with olive oil. Bake salmon in preheated oven for until fish flakes easily with a fork, about 25 minutes.
In a large skillet, heat olive oil over medium heat. Add shallots, stirring occasionally, until translucent. Add garlic and anchovies and continue to stir. Season with black pepper and, if desired, salt.
When garlic has softened and shallots are lightly caramelized, add cooked pasta to the skillet and combine. Deglaze with white wine and reduce for several minutes.
Remove salmon from oven and flake into large pieces. Add to skillet and stir gently to combine. If needed, add some of the reserved pasta water. Garnish pasta with lemon zest and serve.