At least 2 hours before serving, preheat oven to 375°. On a small foil-covered baking sheet, rub beets with about 1/2 tbsp. oil and sprinkle generously with salt and pepper. Bake until a knife point slides in without resistance, about 1 1/2 hours. Let cool until warm, then rub off skin with paper towels. Cut into wedges, drizzle with a little more oil, and set aside in a small serving bowl.
While beets are cooking, put potatoes in a pot, cover with water, add salt to taste, and bring to a boil. Lower heat and simmer until potatoes are tender, 15 to 20 minutes. Drain and set aside.
Make fondue: In a small saucepan over medium-low heat, combine wine, 1/4 cup water, the shallot, garlic, thyme sprigs, bay leaf, and peppercorns. Simmer gently, uncovered, until liquid is reduced to 1/2 cup, about 5 minutes.
Strain through a fine-mesh sieve into a measuring cup and discard solids. Return seasoned wine to saucepan and bring to a simmer over medium-low heat.
Meanwhile, in a bowl, whisk together milk, 1/4 cup water, the cornstarch, salt, and sugar. Whisk milk-cornstarch mixture into simmering wine. Bring to a boil, whisking constantly, until it thickens, 2 to 3 minutes. Reduce heat to low and add cheese, whisking until smooth. Season to taste with salt and keep warm.
To serve, cut apple into thin slices and separate Belgian endive into leaves. Slice any large potatoes in half and arrange everything, along with bowl of beets, on a platter. Pour fondue into a small deep baking dish, sprinkle with thyme leaves, and set on platter.
Make ahead: Beets, up to 3 days, chilled. Fondue, up to 2 days, cooled at room temperature, then chilled with a piece of plastic wrap pressed directly onto surface of fondue. Rewarm in a saucepan over low heat, whisking constantly.
Wine pairing: A crisp, tangy white like Long Meadow Ranch 2014 Sauvignon Blanc (Rutherford, Napa Valley; $22). Its grassy, limestone character brings out the thyme in the fondue, and its zingy citrus keeps step with the goat cheese. This wine is available as part of a special intro offer to Sunset's new wine club, Firstleaf. sunset.com/firstleaf. --Sara Schneider