Heat oven to 400 degrees F. Line a rimmed baking sheet (a jelly roll pan will work) with parchment paper for roasting your vegetables.
Cut the top off of fennel bulb, then cut the bulb in half and remove the hard core at the bottom of each bulb half with your knife using a triangular cut. Cut the fennel in long vertical strips. Clean your red potatoes, cut them in shoestring-like strips. Clean and cut the onions in half, and then each half into vertical strips. Cut the baby carrots in half.
Toss all of the vegetables in a large bowl (or on your pan) with olive oil (about 3-4 tablespoons), thyme, and salt and pepper to taste. Roast vegetables on your lined baking sheet for approximately 40 minutes in the oven until cooked through -- you are not looking for the vegetables to be crispy, just cooked thoroughly and smelling of thyme.
For the Shallot Sauce:
While roasting the vegetables, make your shallot sauce by first removing the shallot skin and cutting the shallot horizontally so you have shallot rings. Put a small sauce pan on the stove and melt 1 tablespoon of butter on medium/low heat. Once the butter is melted, add your shallots and sauté them until translucent, but not crispy. Then stir in the flour and cook and stir this “shallot roux” until it turns a light yellow and bubbles (a few minutes at the most). Then whisk in your chicken broth, turn the burner to low, stirring every few minutes for about 15 minutes total or until the sauce thickens slightly - it should not be a thick as a pudding, but just think enough to coat a spoon temporarily. Once the sauce has thickened a bit, remove it from the heat and stir in the remaining 2 tablespoons of butter and season with salt to taste. This is a delicate sauce, so be careful not to over-salt.
For the Seared Salmon:
Heat your favorite searing/sautéing pan to medium heat, add 1-2 tablespoons of olive oil once hot. Cut your salmon into 4 even pieces (about 6 oz. a piece) and season both sides with salt and pepper. Sear each side in the pan for about 2-3 minutes each side or until it is cooked to your desired done-ness. (I prefer medium with a slight bit of pink in the middle).
Put about a cup and a half of the roasted vegetables in the center of your plate or in a nice pasta bowl. Place the a piece of salmon over the vegetables and top with about a ¼ cup of shallot sauce. Serve, savor and enjoy!