You can keep the finished eggs for up to five days, cool them in an ice water bath for 10 minutes; refrigerate in an airtight container. Reheat at 140°F for 15 minutes.
Prepare a sous vide water bath in a 6- to 8-quart stockpot. Heat the water to 167°F. Using a slotted spoon, lower eggs into the pot. Cover as much as possible with plastic wrap or a cookie sheet; cook 12 minutes. Lower water temperature to 140°F to hold the eggs until you’re ready to start serving, up to 2 hours.
Preheat oven to 175°F to 200°F. Meanwhile, toast bread in a toaster oven or toaster. Divide toast slices among 4 plates; transfer to oven to keep warm (Breakfast is always best served hot, after all.)
Place ham in a large skillet over medium-high, and cook, turning once, until brown, 3 to 4 minutes total. Place 1 ham slice on each toast slice, and return to oven.
Add 2 tablespoons butter and shallot to skillet over medium. When butter is foamy, add spinach and black pepper. Cook, stirring constantly, until spinach is just wilted and beginning to release liquid, about 1 minute. Transfer to a plate; keep warm.
Melt remaining 1 tablespoon butter. Crack 1 sous vide egg into a blender. Add melted butter, lemon juice, yogurt, mayonnaise, and salt. Process on high speed to emulsify. If sauce is too thick, add water, 1 teaspoon at a time, and process until desired consistency is reached. Season with a pinch of cayenne and extra lemon juice, if needed.
Divide spinach among toast slices, forming a ring to cradle eggs. Working with one at a time, crack remaining sous vide eggs onto a plate. Place 2 eggs inside each spinach ring. Drizzle warm hollandaise over each serving; garnish with parsley, black pepper, and cayenne, if desired. Serve immediately.