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. Season the meat side of each piece with a pinch of salt and set aside, skin side up, until ready to cook.
Step 3Cook the bacon over medium-low heat in a medium pot until the fat renders and the bacon starts to sizzle and brown, about 7 minutes. Add the chopped carrots and cook until they begin to soften, about 5 minutes. Add the onion and cook until it is softened and translucent, about 5 minutes.
Step 4Stir in the lentils, coating them with the flavoring mixture. Add the water, stir and bring to a simmer. Add three-fourths teaspoon salt, reduce the heat to a simmer, cover and cook until the lentils are tender, about 40 minutes. They should still be slightly soupy. (The dish can be prepared to this point up to a day in advance; refrigerate tightly covered if more than a couple of hours.)
Step 5Gently reheat the lentils; if necessary, add more water to make them slightly soupy. Stir in the red wine vinegar and black pepper. Taste and adjust seasoning, adding more salt, pepper or vinegar as needed. The mixture should be slightly tangy and sour, to balance the bitterness of the dandelion greens. Stir in the greens and keep warm.
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 7Spoon a pool of about half a cup of the lentil mixture into shallow bowls or pasta plates. Place a salmon fillet in the center of each, crisped skin side up. Sprinkle with a little coarse salt and minced parsley and serve immediately.