Slice salmon into 4 six-ounce portions. Place on a cutting board or baking sheet. Season both sides generously with salt and pepper.
Put cream in a mixing bowl and beat with a whisk until just barely thickened. Add 1/4 teaspoon salt, some freshly ground pepper, the mustard, the cayenne and the lemon zest. Beat again until soft peaks form, but don’t let the cream get too stiff. Fold in chives. Taste and adjust seasoning.
Put butter in a large cast-iron skillet over medium-high heat. When butter begins to foam, add salmon pieces and reduce heat slightly. Cook gently on one side for about 2 minutes, then flip and cook one minute more. Turn off heat and let rest for 2 minutes. Salmon should be cooked through but moist. Be careful not to overcook.
Transfer salmon to a platter or individual plates. Spoon some savory whipped cream over each serving. Garnish with tarragon and watercress.