Preheat oven to 200°C. Line an oven tray with baking paper. Preheat BBQ grill or hotplate to medium-high (if using).
Toss kumara with olive oil on lined tray and season with salt and pepper. Spread out into a single layer and roast for about 20 minutes or until golden and tender.
Place all lemon honey pork ingredients - except the oil and honey - in a bowl and toss to coat pork. Season with salt and pepper, and set aside to marinate.
Meanwhile, make the apple and fennel salad. In a small bowl, whisk together extra-virgin olive oil, vinegar, mustard, honey, lemon juice and yoghurt. Roughly chop cos lettuce; cut apple into quarters, remove and discard core, then thinly slice; discard outer layer of fennel bulb and very thinly slice the white part; peel and shred or coarsely grate carrots. Add all to a large bowl with three-quarters of the dressing (reserve the rest for serving) and toss to combine. Season to taste with salt and pepper.
Heat olive oil in a large fry-pan on medium-high heat. Cook pork for 3-4 minutes on each side until just cooked through. Turn off the heat and drizzle honey over pork. Quickly turn pork in pan to coat in the honey then set aside to rest for 5-10 minutes.
Place roast kumara in a bowl and use a fork or potato masher to very lightly crush the kumara. Fold through red onion, parsley and feta. Season to taste with salt and pepper.
Thinly slice pork, reserving any resting juices.
To serve, divide kumara feta crush and apple fennel salad between plates. Top with slices of pork and drizzle with any resting juices and remaining yoghurt dressing.