Preheat your oven to 350°F. While it heats, cut the pita rounds into 1-inch squares and toss them in a bowl with 1.5 tablespoons of olive oil and 1/4 teaspoon of salt until evenly coated. Spread them in a single layer on a baking sheet and bake for 10 minutes, stirring halfway through to ensure even browning. The chips should be golden and crispy—this step creates texture contrast and prevents the salad from becoming soggy. Set aside to cool while you prepare the remaining components.
In a small bowl, whisk together the red wine vinegar, lemon juice, garlic, Dijon mustard, sugar, oregano, 1/4 teaspoon salt, and black pepper. Once combined, slowly drizzle in the 3 tablespoons of olive oil while whisking constantly to emulsify the dressing—this creates a cohesive sauce rather than separate oil and vinegar layers. I use Dijon mustard specifically because it acts as an emulsifier and adds a subtle tangy depth to balance the acidity. Let the dressing sit while you prep the vegetables.
Peel the cucumber and slice it into 1/4-inch half-moons for consistent bites. Halve the cherry tomatoes lengthwise—this orientation distributes them better throughout the salad and looks more appealing. Dice the red onion into bite-sized pieces. Crumble the feta cheese by hand into chunks rather than using a grater; I find this gives a better texture that doesn't get lost in the salad. Have all components ready before assembling so the salad comes together quickly.
In a large bowl, combine the spring mix, prepared cucumber, halved tomatoes, diced red onion, kalamata olives, and cooled pita chips from Step 1. Pour the vinaigrette from Step 2 over the salad and toss gently but thoroughly to distribute the dressing evenly. The key is tossing right before serving so the pita chips stay crispy and the greens don't wilt. Top with the hand-crumbled feta cheese from Step 3 and serve immediately while the pita chips are still crunchy.