Preheat oven to 325F Line a baking sheet large enough for your fish with foil.
Arrange your fish on the foil and brush with olive oil. Season lightly with sea salt. Bake for 30 minutes, then turn off the heat and let the fish sit in the oven for another 10 minutes, without opening the door. Remove the salmon and let cool, then chill until ready to serve.
Make the dressing: add the yogurt, mayo, lemon, and both dills to a small food processor and process until smooth. Taste and season with salt and pepper. Add more lemon if necessary.
When the fish is chilled, arrange your platter. Spread a layer of greens across the whole plate. Lay the salmon in the center. If the salmon is too large, trim a bit off the tail end with a sharp knife.
Arrange the rest of the veggies around the salmon. I like to add some lemon slices to the top of the fish. Sprinkle the capers and dill over all. Tuck in a few pretty edible flowers if you have them.
Serve the salmon asap after arranging your salad, along with the dressing on the side. The delicate spring greens will not last very long after arranging. If you must store it for a short while, wrap in plastic before refrigerating, and add the garnishes just before serving.