Evenly coat each portion with salt and pepper.
Sprinkle chopped rosemary across presentation side of fish pieces
Smear salmon with a generous coating of the mustard, also only on the presentation side.
Heat sauté pan on stove over high heat until a drop of water dances across the surface, and evaporates in seconds.
Add olive oil to pan, allowing it to coat the surface and heat through.
Gently place salmon in pan, mustard side down. Allow it to sear on high for 15 seconds before reducing heat to medium high.
Watch the edges of the fish. When they have become opaque almost to the side facing you, it's time to flip, about 3 to 5 minutes.
Work the offset spatula under the fish carefully, so as not to tear the crust formed by the mustard, and then flip over each piece.
Reduce heat again to medium, cover the pan to allow fish to cook through., about 3 to 5 minutes.
Using a thermometer, measure the temp at the thickest part. For medium rare, 100 to 110, medium, 120 degrees.
Remove from pan, plate with lemon slices.