Preheat your oven to 450°F; place the salmon on a rimmed baking sheet or baking dish; drizzle with a little bit of olive oil and sprinkle with salt and pepper. Roast in the preheated oven until the flesh turns opaque and the top starts to brown, about 10 to 15 minutes.
While the fish is in the oven, heat a splash of olive oil in a saute pan set over medium heat then add the shallot and garlic. Cook until golden then add the chicken stock and bring to a simmer; simmer for about a minute than whisk in the grainy mustard.
In a small container, dilute the corn starch in the milk and then add this to the simmering sauce; whisk until well incorporated and the sauce is thickened, about 45 seconds, then kill the heat and whisk in the fresh chives.
Remove the roasted salmon from the oven and serve, topped with a few tablespoons of the sauce. Garnish with more chopped chives, if desired.