Preheat oven to 375°F; start convection fan if available. Cut off top third of garlic heads to expose cloves. Place garlic on small baking sheet, cut side facing up, and drizzle with olive oil. Bake until cloves have softened and are lightly browned, 45 minutes. Let cool enough to handle.
Gently squeeze garlic cloves into small bowl, discarding skins. Whisk in yogurt, lemon zest and juice, salt and hot pepper flakes. Scrape into fine-mesh sieve lined with folded cheesecloth and set over small bowl. Cover with plastic wrap, refrigerate and let drain for 24 hours. Discard whey (liquid in bowl). Transfer garlic labneh to a resealable container and refrigerate for up to 5 days.
Root Vegetable Pavé
Preheat oven to 350°F; start convection fan if available. Lightly oil 13 x 9-inch baking pan; line bottom with parchment paper.
Using a mandoline, thinly slice the potatoes lengthwise. Form a stack with some of the larger pieces and cut in half lengthwise to form straight edges. Gently toss potatoes in bowl with 1 tsp each of the canola oil and thyme, salt and pepper.
Arrange a thin, even layer of potatoes in bottom of baking pan, fitting straight edges to sides of dish and filling centre with remaining slices. Continue layering, evenly and precisely, with remaining potato slices, pressing firmly as you go.
Continue forming distinct layers of each root vegetable in succession. Slice carrots, parsnips, turnip, sweet potatoes and celery root lengthwise, then toss each with canola oil, thyme, salt and pepper before layering and pressing. Cover tightly with foil. Top with a baking sheet to weigh down vegetables and fully seal edges. Bake until tender, 2 hours.
Remove foil and place a layer of plastic wrap or parchment paper directly on surface. Top with a second baking pan that fits just inside the dish, lightly pressing it down. Refrigerate overnight with the dish weighing down the pavé (see note).
Rosemary Beet Purée:
Using a juicer, juice half of the beets to make ½ cup beet juice; discard pulp. Quarter the remaining beets. Transfer beets and juice to small saucepan; add red wine vinegar and rosemary. Bring to a simmer over medium-high heat. Cover, adjust heat and simmer until tender, 15 minutes.
Transfer beet mixture to high-speed blender. Add canola oil, salt and hot pepper flakes; purée until smooth. Taste and adjust seasoning. Transfer to a resealable container and refrigerate for up to 3 days.
To serve:
Preheat oven to 425°F; start convection fan if available. Line baking sheet with parchment paper.
Run paring knife around edge of pan to release pavé. Top with baking sheet and flip to invert pavé. Lift away baking dish and peel off parchment. Cut into 6 large or 12 small rectangles; place on a baking sheet and bake until heated through, 15 minutes, or reheat in microwave. Serve with rosemary beet purée and roasted garlic labneh.
Notes
This dish may be served directly from the oven, but for show-stopping presentation, it’s best to refrigerate it overnight until firm. Then it’s easy to cut into precise shapes and reheat.