Bring a large pot of water to a boil and season generously with salt so it tastes lightly salty.
Add the short pasta to the boiling water and cook according to the package directions until al dente, usually about 10 to 12 minutes.
While the pasta cooks, heat 2 tablespoons of the extra-virgin olive oil in a large skillet over medium-low heat.
Add the minced garlic to the skillet and cook gently for 1 to 2 minutes, stirring often, until fragrant but not browned.
Stir the halved cherry tomatoes into the skillet and cook for 2 to 3 minutes, just until they start to soften and release a little juice.
Add the sliced Kalamata olives to the skillet and cook for 1 minute, stirring to combine with the tomatoes and garlic.
Sprinkle in the dried oregano, dried thyme, salt, and black pepper, and stir to coat the tomatoes and olives evenly with the seasonings.
When the pasta is al dente, reserve 2 tablespoons of the pasta cooking water, then drain the pasta well.
Add the drained pasta directly to the skillet with the tomato and olive mixture and toss gently to combine over low heat.
Pour in the reserved pasta cooking water, the remaining 1 tablespoon of olive oil, and the fresh lemon juice, then toss again until the pasta is lightly coated and glossy.
Remove the skillet from the heat and gently fold in the crumbled feta cheese so it is evenly distributed throughout the pasta.
Sprinkle the sliced fresh basil over the pasta and toss once more, adjusting salt and pepper to taste if needed before serving.