1. Place all pesto ingredients in a food processor; process until smooth.
2. Break eggs into individual ramekins or small bowls without breaking the yokes. Heat about 1½ inch of water in a medium nonstick skillet over medium heat. Bring water to a gentle simmer, and then reduce heat to low. The water should barely be simmering. Add vinegar to the pan. This will help hold the eggs together. Using a spoon, stir the water in the pan around the edges to create a gentle whirlpool in the center. Holding the ramekin close to the surface of the water, gently pour an egg gently into the center of the whirlpool. Let the egg cook undisturbed until the egg is set, 3 to 4 minutes. Using a slotted spoon, transfer the egg to a folded paper towel on a plate. (If the egg sticks to the pan, gently free it with a spatula.) Continue with the remaining eggs. (Or use a stainless steel egg poacher if you want to make it easy!)
3. When you are ready to assemble the dish, place ¼ cup salad greens on individual plates. Slice the cherry tomatoes in half and add them to the salad greens. Top with a slice or two of the salmon, followed with an egg. Sprinkle eggs with a pinch of salt and pepper. Top this off with a spoonful of pesto.