Bring butter to room temperature. Chop hazelnuts roughly and mash with butter and lemon together in a small bowl. Taste and season with more salt and / or lemon if needed (you probably won’t).
Heat a medium frying pan large enough to just hold the fish in a single layer on a medium high heat. Season fish with salt. Add a splash of oil to the pan and cook fish for 2-4 minutes on each side. You want the fish to be golden brown on the surface and the flesh to look opaque and no longer translucent when you cut into it.
Divide fish between two plates. Top with hazelnut butter and allow it to melt onto the fish to create a delicious sauce. Serve salad leaves on the plates and use the melted butter to dress the salad as you eat.