Bring a big pot of salted water to a boil. Blanch the cauliflower florets for 30 seconds and remove with a slotted spoon. Set aside.
In the same pot of water, cook the pasta until just tender. Drain, toss with cold water and set aside.
In a large bowl of a food processor, combine the yogurt, ricotta, mayonnaise, garlic, lemon juice, lemon zest, anchovy paste, 1/2 cup of the crumbled feta, basil and mint. Blend until smooth. With the processor running, slowly pour in the olive oil until emulsified. Season to taste with salt and pepper.
Toss the pasta with the yogurt dressing and gently fold in the remaining feta, the artichoke hearts, green olives, capers and cherry tomatoes. Garnish with remaining basil.