Step 1Place the salmon skin-side-up on a cutting board. Run the back of a knife over the skin, using a squeegee motion. As moisture emerges from the skin, wipe the skin and the knife dry with a paper towel. Repeat until no more moisture is visible.
Step 2Turn the salmon over and feel along the surface of the flesh with your fingertips just above and below the midline. If you feel pin bones, pluck them out with tweezers or needle-nose pliers. Slice the fillet in half lengthwise and then into fourths crosswise to make 8 fillets. Season the meat side with salt and set aside, skin-side-up, until ready to cook.
Step 3Slice the bacon into thin crosswise strips. Cook them in a large nonstick skillet over medium heat until they are slightly crisp and the fat has rendered, about 10 minutes. Remove the bacon with a slotted spoon and reserve, leaving the fat in the pan.
Step 4While the bacon is cooking, trim the mushroom stems and cut the mushrooms into lengthwise quarters. Cook the mushrooms in the rendered bacon fat until they color slightly, 2 to 3 minutes. Add the shallots and cook until they soften but do not color, 2 to 3 minutes.
Step 5Return the bacon strips to the pan and add the thyme and the white wine and cook until the wine has reduced to a thin glaze, about 5 minutes. Add the cream and the peas and cook just until the peas soften; this will take 5 to 10 minutes for fresh peas depending on their starchiness, and about 5 minutes for frozen. Remove from heat until ready to serve.
Step 6Heat another large nonstick skillet over high heat and add just enough oil to film the bottom of the pan, about 1 to 2 tablespoons. When the oil is hot enough to sizzle, place the salmon fillets in the pan skin-side-down and reduce the heat to medium. Cook until you see the cooked color come about one-third of the way up the side of the fillet, 3 to 5 minutes. Remove the pan from the heat and turn the salmon over to finish cooking off the heat while you prepare the plates.
Step 7Briefly return the peas and mushrooms to high heat and stir in the butter. Season to taste with salt. Divide the mixture among 8 shallow pasta bowls and place a piece of salmon skin side up in the center of each. Serve immediately.