Cover potatoes with water and bring the water to a boil. Salt the water and simmer potatoes 10 to 12 minutes, until just tender. Drain potatoes and return to warm pot to dry the potatoes. Drizzle potatoes with a little oil to keep them from discoloring and to shine them up.
Fill a second skillet or saucepan with 2 inches of water. Cover and bring the water to a boil on the stovetop. Salt the water, replace the cover and reduce heat to simmer.
To a heavy saucepan over moderate heat, add 1 tablespoon oil and the chopped shallots. Saute shallots for 2 or 3 minutes, then add sherry and allow it to almost evaporate, a minute or two. Add half-and-half to the pan and reduce heat to low. Cut cream cheese into 1-inch slices and add it to the pot. Allow the cream cheese to slowly melt into the half-and-half, 5 minutes. Add Parmesan and shredded Gruyere or Swiss to the sauce and stir until cheese is melted and fully incorporated. Stir in lemon juice. Season sauce with, nutmeg and black pepper. Place a candle underneath a wire rack or warm a fondue pot. Transfer cheese sauce to fondue pot or place saucepan over wire rack and burning candle.
To simmering, salted water, add broccoli and cook florets, covered, 3 minutes. Remove broccoli with a slotted spoon to a plate and add asparagus tips. Cook asparagus tips 2 minutes, then remove with tongs to a plate.
Arrange the items for dipping on a large serving platter. Garnish the cooked potatoes with chives. Set the cubed baguette on the opposite end of the platter, to balance color. Between potatoes and bread, arrange cooked broccoli, asparagus and cherry tomatoes. Set out fondue forks or bamboo skewers for dipping. Place small dishes of cornichons, marinated mushrooms and pickled onions near dipping station for accompaniments.