Whisk the olive oil, red wine vinegar, lemon juice, garlic, oregano, salt, and pepper in a small bowl until cloudy and combined.
Pour about a third of the dressing over the steak in a zip-top bag and turn to coat. Let it marinate 30 minutes at room temperature while you prep the salad. Reserve the remaining dressing.
Cook and Rest the Steak
Heat 1 tablespoon olive oil in a heavy skillet over medium-high heat until it shimmers.
Pat the steak dry, season lightly with salt and pepper, and sear 3 to 4 minutes per side for medium, or until it reads 145F on a thermometer.
Transfer to a cutting board and rest 5 to 10 minutes before slicing.
Build and Dress the Salad
Toss the romaine, cucumber, tomatoes, red onion, and olives in a large bowl.
Slice the rested steak thinly against the grain and lay it over the salad.
Crumble the feta over the top, scatter the parsley, and drizzle with the reserved dressing just before serving.
Notes
Slice against the grain: Cut the steak across the muscle lines for tender strips.
Dress at the last minute: Dressing too early wilts the greens.
Serve the steak warm: Warm steak against the cold salad is the whole point.
Swap the protein: Grilled chicken, shrimp, or chickpeas all work in place of steak.