Step 1

In a bowl, mash together goat cheese, 2 tablespoons oil, 1 teaspoon lemon juice, and oregano. Season with salt and pepper. Pulse half of salmon to a paste in a food processor. Add 2 cups spinach, remaining salmon, lemon zest, 1 1/4 teaspoons salt, and 1/2 teaspoon pepper; pulse to barely combine. Shape mixture into four 3/4-inch-thick patties.

Step 2

Toss together cucumber, tomatoes, and remaining 2 cups spinach. Add 2 tablespoons oil and remaining 1 tablespoon lemon juice. Season.

Step 3

Heat a large nonstick or cast-iron skillet over medium-high. Add remaining 2 tablespoons oil. Cook patties until golden and cooked through, 3 to 4 minutes a side. Serve alongside salad with goat-cheese mixture, flat-bread, and lemon wedges.