In a large Dutch oven over medium-high heat, add the butter. Add the fennel and sugar and cook for 3 to 4 minutes until the fennel caramelizes. Add the cider, stock and thyme. Cook until the fennel is tender and liquid is reduced, about 10 minutes Season the fennel with salt and pepper, to taste. Add the parsley and mix well. Remove from the heat and cover.
In a small saucepan, add the cider, cayenne and brown sugar and cook over medium heat until 1/2 cup of liquid remains. Set aside.
In a large saute pan over medium-high heat, add the oil. Season the salmon fillets with salt and pepper, to taste, and sear for 4 minutes in the hot oil. Remove from the pan and put, seared side up, on a quarter sheet tray with a rack. Spoon the glaze over the top of each fillet and bake until cooked through, about 4 minutes. Remove from the oven to a serving platter and serve with the braised fennel alongside.