Preheat oven to 375 degrees.
Generously salt the top of the salmon with sea salt or kosher salt. Cut the whole salmon filet in half so both pieces will fit in the pan.
Let salmon rest with salt for 30 minutes.
After 30 minutes, rinse the salt off your salmon and pat dry.
Heat your oven safe skillet on your cooktop. Melt butter and oil together. Place salmon in pan skin side down if your salmon filet has skin. Let the salmon sear on the cooktop for about 3 minutes.
Transfer the skillet into the preheated oven and let the salmon cook at 375 degrees for 3 minutes.
Reduce oven temperature to 300 degrees and let salmon cook for an additional 10 minutes or until salmon is cooked the way you like.
Remove skillet and plate salmon.
Can be served with bearnaise sauce or lemon wedges.