Preheat oven to 375°F. Melt butter in an oven-proof pot or dutch oven (4-6 quart) over medium heat. Once melted, add the veggies, and sauté until tender, about 2-3 minutes. Deglaze the pan with vermouth, add the whole grain mustard, and whisk to combine. Bring to a simmer, and, once the vermouth has reduced by half, add the flour and stir to coat the veggies. Add broth and milk to the pot, whisk to combine, and bring to a simmer. Simmer for 5-8 minutes, whisking frequently, or until the mixture has slightly thickened. Season the base to taste with salt and pepper. Add the salmon, cod, shrimp, and scallops to the pot, and gently stir to combine. Remove the pot from the heat and evenly top with the mashed potatoes. Sprinkle the remaining cheese over the potato topping and place in the oven.