Juice the beet cubes with a vegetable juicer. Strain the juice, add it to a pot and heat to just below a simmer.

Cut each half of the pears into ¼-inch slices and add them to the beet juice. Slowly poach for about 10 minutes, until slightly tender but not mushy. When ready, cool the entire mixture in an ice-water bath. Store for up to 4 days.

Clean the carrots under cold water, scrubbing lightly with a clean (new is best) sponge or scrub pad to remove any dirt or debris. Using a vegetable slicer or sharp knife, cut the carrots into thin, round slices about ⅛-inch thick. Reserve and cover with cold water to store.

Place the cinnamon stick and the orange peels in a cheesecloth bag and secure. Add the cranberries, sugar, vinegar, beer and salt to a medium saucepan with the bundle of aromatics and cook on low heat for 3 to 4 hours, stirring regularly. Check that the flavor is balanced, adjust with salt or more vinegar, if needed, then cool and store in the refrigerator for up to 1 week.

Add the mascarpone, honey, and lemon juice to a medium-size mixing bowl and whisk until smooth. Next, soak the wood chips in water for 5 to 10 minutes, then remove from the water and place in a small aluminum or stainless-steel pan lined with aluminum foil. Place this pan inside a larger hotel pan, or any metal pan with tall sides.

Transfer the cheese mixture to a small, wide pan that will also fit inside the hotel pan, alongside the pan with the wood chips. Using a butane torch, ignite the wood chips and then cover the entire hotel pan with foil, making sure all edges are sealed tightly. Allow the cheese to smoke for 1 hour, relighting the wood chips every 20 minutes.

Heat the oven to 350°. Using the paddle attachment of a stand mixer, cream the butter slowly. Separately, combine dry ingredients and sift. Slowly add dry ingredients to the creamed butter while mixer is on low speed. Mix until everything is homogeneous. Whisk the egg yolks together gently, then fold them into the flour dough.

Dust a smooth dry surface with a few tablespoons of flour and, using a rolling pin, roll out the dough to an even ½-inch layer. Using a small ring mold cutter (4 inches in diameter), punch out small rounds of the tart dough. Line a baking sheet with parchment paper and grease with butter. Arrange the tarts at least 1-inch apart and bake at 350° for about 10 minutes, until golden brown. Let the tarts cool.

To serve, spread the smoked mascarpone cheese all over the top of the tarts. Next, alternate circles of the prepared pears and carrots, while arranging in a circular pattern around top of tart, until top is completely covered. Add a small amount of relish to the top then season with flaky sea salt and drizzle with extra-virgin olive oil. Garnish with fresh mint and tarragon.