To make the dill oil, put the oil and dill in a blender and puree for a solid minute on high. Set some cheesecloth in a fine-meshed strainer and put the strainer over a bowl. Pour the oil into the strainer and put the whole thing into the fridge to slowly drip.
Salt the salmon pieces and put in the fridge.
Gently cook the onion in the walnut oil until it is soft and translucent. Don't let the onions brown. When they are cooked, puree them in a blender and set them aside.
Slice each cucumber lengthwise. Use a spoon to scrape out all the seeds from both cucumbers; don't toss the seeds. Chop the unpeeled cucumber and put it and the seeds into a blender. Puree and strain for 2 hours.
Whisk the strained cucumber water into the pureed onions to make a sauce the consistency of melted ice cream. Add 2 tablespoons of the dill oil and season with lemon juice, salt and white pepper to taste.
Heat the oil in a pan over high heat until it's almost smoking. Pat the salmon dry and sear one side for 6 to 8 minutes. Flip if necessary to finish cooking.
Toss the diced cucumber and cherry tomatoes in the sauce and pour some in shallow bowls or plates. Set the salmon on top seared side up and top with dill and salmon caviar if desired.
