Toast pine nuts in a dry skillet over medium heat for 2-3 minutes until golden and fragrant, then set aside.
In a small bowl, whisk together 0.5 tbsp olive oil, lemon juice, red wine vinegar, minced garlic, dried oregano, and half of the sea salt and black pepper.
Pat the skirt steak dry with paper towels and season both sides with the remaining sea salt and black pepper.
Heat 1 tbsp olive oil in a heavy skillet over high heat until shimmering.
Sear the steak for 3-4 minutes per side for medium-rare, then transfer to a cutting board to rest for 5 minutes.
While the steak rests, toss the arugula, spinach, sliced cucumber, and thinly sliced red onion in a large bowl with the prepared dressing.
Slice the rested steak against the grain into thin strips to ensure maximum tenderness.
Top the dressed greens with the steak strips, crumbled feta cheese, and the toasted pine nuts before serving.