Skin salmon then cut the fillet in half lengthwise into two, long 1/2-inch thick pieces. Then cut these long, thin fillets into 3-inch wide pieces. (see notes)
Mix the Dijon mustard and dill together in a shallow bowl.
Dredge salmon in the mustard dill sauce.
Warm frying pan over medium-high heat and add oil or butter.
Cook salmon 1-2 minutes on each side until done to your liking.
Season to taste with lemon juice and a of couple grinds of black pepper.
Serve and garnish as desired.