Shred cucumber with a box grater. Set in a strainer to drain.
Brush 2 teaspoons oil in a large cast-iron skillet and heat over medium high until shimmering. Sprinkle ½ teaspoon salt and pepper all over the salmon. Lay salmon filet skinned side up in the hot oil. Let cook, undisturbed until browned and crispy along the bottom edge, and the salmon is opaque about half way up the side of the filet, 2 ½ to 5 minutes, depending on thickness. Flip salmon over and remove the skillet from the heat. Allow the salmon to remain in hot skillet to allow the carry-over heat to continue cooking the other side to desired doneness, 2 to 4 minutes. Transfer salmon to a plate and cover with foil to keep warm.
Squeeze excess liquid from the cucumber. Add cucumber to a medium bowl and add garlic, Green Mountain Creamery Plain Greek Yogurt, herbs, the remaining 1 teaspoon olive oil, the remaining ¼ teaspoon salt and pepper to taste. Whisk to combine.
Serve the salmon topped with the tzatziki sauce.