For the fennel: In a medium saucepan, cover the fennel with cold salted water. Place over high heat, bring to a boil, and then lower to a simmer. Cook until very tender, about 10 minutes. Drain well and place in a food processor. Add the olive oil, yogurt and salt. Puree until smooth, scraping down the sides as needed.
For the salmon: Heat the olive oil in a large skillet over medium-high heat. Sprinkle the salmon fillets with the salt. Place the fillets in the pan, flesh-side down, and sear undisturbed for 3 to 4 minutes to create a golden brown crust. Gently flip, and cook for another 2 minutes.
Salad: In a small bowl, mix together the chopped fennel fronds and parsley and the crispy capers.
To plate, spread a little of the fennel puree on each of 4 plates. Top with a salmon fillet. Place a little salad on top of each salmon. Squeeze a bit of lemon over the top if desired. Serve immediately.
Heat 1/4-inch vegetable oil in a small, straight-sided skillet over medium-high heat until it shimmers when swirled. (You can make sure the oil is hot enough by adding one caper to the oil; if it immediately starts to sizzle and pop, the oil is hot enough.) Add the capers to the hot oil and fry until they have popped open and turned golden brown and crispy, about 1 minute. With a slotted spoon, remove the capers to a paper-towel-lined plate to drain.