In the bowl of an electric mixer fitted with the whisk attachment, combine the cream and sour cream. Mix on low until fully combined. Cover the mixing bowl with plastic wrap or a kitchen towel (the mixture splatters as it churns). Beat on medium-high speed until it forms very thick peaks, about 10 minutes. Increase speed to high and beat until the mixture separates into thick, pale yellow butter and thin, watery buttermilk, another 5-10 minutes. Strain the mixture through a colander and drain off all the buttermilk.

Clean the mixing bowl and put the butter back into it. Add the lemon zest, dill, capers, salt, and pepper. Mix on low until combined. Transfer to a small serving bowl, cover, and refrigerate until 30 minutes before serving time. Let sit at room temperature for 30 minutes before serving.

Place the salmon on a platter. Garnish with dill sprigs and lemon wedges. Serve with the dill caper butter and soda bread.