First, you need to prepare a court bouillon to poach the salmon: combine the water, wine, tarragon stems (leaves reserved), bay leaves, peppercorns, and carrot. Bring to a boil over high heat, then decrease the heat to low. Simmer gently for 15 to 20 minutes. Season with salt and pepper.
Then, we set aside some of the liquid to chill the salmon instead of letting it cool in the hot liquid which would overcook it, or, cooling it in cold water which would dilute the flavor. Fill a large, heavy-duty sealable plastic bag filled with ice cubes. Place a bowl over a bowl of ice and transfer several cups of the court bouillon in a bowl. Place the ice pack in the bowl of broth; move the pack around until the broth is well chilled (drain the bag and add more ice to it as needed). Set the chilled court bouillon aside.
Return the heat to high and bring the remaining mixture to a rolling boil. Add the salmon fillets. Cover and simmer for 7 minutes.
To chill the salmon: Remove from the heat and remove the salmon from the poaching liquid. Transfer to the chilled court bouillon and allow the salmon to cool in the bouillon. Cover the fish and broth with plastic wrap and chill in the refrigerator for 1 to 2 hours, or until you are ready to serve. (This helps boost the flavor and allows you to make it ahead without it drying out. )
For the mustard sauce: Meanwhile, put the mustard in a small bowl. Whisk the olive oil into the mustard in a slow, steady stream. Stir in the reserved chopped tarragon leaves. Taste and adjust for seasoning with salt and pepper.
When you are ready to serve, put the greens in a bowl. Drizzle with olive oil and season with salt and pepper. Toss to combine. Arrange the greens on a platter Remove the salmon from the broth and pat dry with paper towels. Top the greens with the salmon and garnish with the sliced cucumber. Serve, passing the mustard sauce separately.