Fill a 5 to 6-quart pot two-thirds full with water and bring it to a boil over medium-high heat. Add 1 tablespoon kosher salt and the rotini pasta.
Cook until al dente, following package directions. Drain and rinse under cold water to stop the cooking. Let it drain completely.
While the pasta cooks, halve the cherry tomatoes. Dice the cucumbers and all three bell peppers into small, even pieces for uniform texture and color.
In a small bowl or jar, whisk together olive oil, lemon juice, Dijon mustard, minced garlic, fresh basil, salt, and black pepper.
Whisk until well combined and slightly thickened. If making ahead, shake before using.
In a large bowl, combine the drained pasta, tomatoes, cucumbers, and all diced bell peppers. Toss gently. Sprinkle crumbled feta on top but don’t stir it in yet.
Pour the dressing evenly over the salad. Gently toss everything together, mixing just enough to coat and distribute the feta without breaking it apart. Chill for 30 minutes before serving for best flavor.