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Make your smoky brown butter: Add the butter to a small saucepan set over medium heat. Do not leave your stovetop perch! Watch as the butter melts, then foams, then begins to brown, swirling occasionally as you go. The whole process should take about 4 minutes, but its really an eyeball (and an aromatic) thing: As soon as it starts to smell nutty and you start to see the brown speckles at the bottom of the pan, remove the pan from the heat so the butter doesn’t burn. Stir or whisk in the smoked paprika and a pinch of sea salt and set aside.
Heat a cast-iron skillet over medium-high heat and add olive oil. Season the fish with salt and pepper, then pan-fry for about 3 to 4 minutes total, flipping once half-way through. (To measure doneness, the fish should feel firm to the touch but not mushy or rock hard.)
Remove filets to dinner plates and spoon a tablespoon or two of smoky brown butter on top as shown.