Preheat the oven to 190ºC/375ºF/gas 5.
Bring three pans of salted water to the boil. Peel the potatoes and carrots and scrub the beets.
Cut any large potatoes in half and leave any small ones whole. Place the potatoes in one of the pans and parboil for 5 to 10 minutes, or until half cooked. Drain the potatoes, then leave them to steam dry. Return the potatoes to the hot pan and shake it around to chuff up the edges.
Repeat with the carrots and beets but do not shake them around after, leaving them to steam dry.
Pick the rosemary leaves and scatter over the potatoes. Break up and scatter with half of the garlic cloves, unpeeled, a drizzle of olive oil, and a pinch of sea salt and black pepper, then place in a large roasting tray.
Place the carrots and beets in the tray, keeping everything separate, then drizzle over a good lug of olive oil and season well with salt and pepper.
Scatter over the remaining garlic cloves and roast all the veg in the hot oven for about 20 to 30 minutes, giving them a jiggle every so often, or until everything is crispy, golden and delicious – about 10 minutes before they're ready, drizzle the honey over the carrots and add a lug of balsamic to the beets, then return to the oven.
For extra crispy roasties, gently squash them with a potato masher or fish slice when there's about 5 minutes to go – it's a great trick to make them taste even better.