Remove the ribs from the kale and tear the leaves into 1-inch pieces, then set aside. Remove the stems from the basil and discard (you'll only need the leaves). Peel the garlic cloves. Bring a large pot of salted water to a boil and add the pasta, cooking it to al dente according to package directions (usually 8-10 minutes). While the pasta cooks, you can prep the remaining ingredients. Drain the pasta in a colander and spread it on a clean kitchen towel or parchment paper to cool slightly—this prevents it from clumping and allows it to absorb the dressing better.
Add the basil leaves, garlic cloves, olive oil, white wine vinegar, dried oregano, salt, and black pepper to a food processor. Blend until smooth and emulsified, stopping to scrape down the sides as needed—you want a cohesive dressing with no large chunks. Taste and adjust seasoning if needed. I like to add a crack more black pepper than the recipe calls for to give it a nice peppery kick that complements the kale beautifully.
Place the torn kale in a large mixing bowl and drizzle with about 1 tablespoon of olive oil (from any leftover or a separate measure). Using your hands, massage the kale vigorously for 1-2 minutes, working the oil into the leaves until they become darker, softer, and more pliable. This process breaks down the kale's cell structure, making it more tender and better able to absorb the dressing flavors. Set the massaged kale aside in the bowl.
To the bowl with the massaged kale, add the cooled pasta from Step 1, the sun-dried tomatoes, parmesan cheese, and feta cheese crumbles. Toss everything together gently to combine all the components evenly. At this point, the salad looks relatively dry, but that's perfect—the dressing will be absorbed as it sits.
Pour the basil-garlic dressing from Step 2 over the salad and toss well, making sure every ingredient gets coated evenly. Cover the bowl with plastic wrap or a lid and refrigerate for at least 1 hour before serving. I find that letting it chill actually improves the flavor—the kale continues to soften and all the Mediterranean flavors meld together beautifully. You can make this up to 4 hours ahead, which makes it perfect for meal prep or entertaining.