Slice the cauliflower into large florets with a knife so that the flat side of the florets can make full contact with the pan and caramelize during baking.
Dice the potatoes into 1/2-inch cubes and slice the carrots crosswise, about 1/3-inch thick. Place on a large rimmed baking sheet, drizzle with olive oil and sprinkle with paprika and salt. Toss vegetables to coat and spread out on the pan.
Bake for 30 minutes, shaking and turning the pan halfway through. When the vegetables are tender and easily pierced with a knife, remove from the oven and toss with feta and parsley. Serve hot.
A great side for a grilled chicken breast or tempeh steak, these baked veggies with feta can also be a main dish, served over orzo pasta, brown rice or polenta.