Dice the red onion finely and set aside. Slice the cherry tomatoes in half, slice the kalamata olives into thirds, and measure out the green olives. Crumble or cut the feta cheese into bite-sized pieces, reserving about 2 oz for garnish. Slice the fresh basil into thin ribbons and set aside. Having everything prepped before cooking ensures the dish comes together smoothly without scrambling for ingredients mid-cook.
Combine the orzo and chicken stock in a medium saucepan and bring to a boil over medium-high heat. Once boiling, reduce the heat to medium-low, cover with a lid, and simmer for 10 minutes, stirring once halfway through cooking at the 5-minute mark. The orzo will absorb the flavorful broth and become creamy, similar to risotto. I like using chicken stock instead of water because it builds flavor right into the pasta from the start.
In a small bowl, whisk together the lemon juice, olive oil, smoked paprika, and Italian seasoning to create a simple vinaigrette. When the orzo is tender and most of the liquid has been absorbed (after the 10-minute simmer), remove from heat and stir in the prepared tomatoes, olives, and most of the feta cheese from Step 1. Pour the vinaigrette over the mixture and gently stir to combine all ingredients, distributing the flavors evenly throughout.
Return the pan to low heat and stir gently for 1-2 minutes to warm the mixture and allow the flavors to meld together. Taste the dish and season with salt and pepper to your preference, starting with a light hand since the feta, olives, and broth already contribute saltiness. For a more cohesive dish, I like to let it warm through on low heat rather than serving it cold, which helps all the components meld beautifully.
Transfer the warm orzo to a serving platter or individual bowls. Top with the reserved feta cheese from Step 1 and the fresh basil ribbons just before serving. The cool, creamy feta and bright basil provide a fresh contrast to the warm, savory pasta.