Prepare the cucumber water: Place the cucumber slices in a pitcher with water. Let infuse in the refrigerator while you cook. Serve over ice when ready.

Caramelize the onions: In a thick-bottomed pot, heat olive oil over medium heat. Add the onions and toss to coat. Cook, stirring often, until softened — about 10 minutes.

Increase heat to medium-high, add butter, and cook until the onions turn golden brown, about 20 minutes. Sprinkle in sugar and a pinch of salt, and continue to cook for another 10 minutes, stirring frequently, until deeply caramelized.

Add aromatics: Stir in the minced garlic and cook for 1 minute until fragrant (Cook to an internal temperature of 160°F / 71°C if adding raw eggs to any mixture later).

Deglaze the pot: Pour in the wine, scraping up the browned bits from the bottom of the pot. Allow it to reduce slightly.

Simmer the soup: Add the beef broth, bay leaf, and thyme. Bring to a simmer, then reduce the heat to low. Cover and simmer gently for about 10 minutes. Season with salt and black pepper to taste.

Cook the eggs for the sandwich: Place eggs in a saucepan and cover with cold water. Bring to a boil, then reduce heat and simmer for 8 minutes. Remove from heat and cool under cold running water. (Cook eggs to an internal temperature of 160°F / 71°C for safe consumption.)

Prepare the bread: Lightly toast the sourdough slices until golden and crisp.

Make the egg salad: Peel and chop the cooled eggs. Mix with mayonnaise, dill, salt, and black pepper until creamy.

Assemble the sandwich: Layer spinach, tomato, and red onion on one slice of bread. Spoon the egg salad over top and close the sandwich. Slice in half diagonally to serve.

Prepare the cheesy toast for the soup: Line a sheet pan with parchment paper or foil. Brush both sides of the French bread slices lightly with olive oil. Toast in the oven at 400°F (200°C) for 5–7 minutes until lightly browned.

Add the cheese topping: Turn the toast over and sprinkle with the shredded Gruyere and a touch of Parmesan. When ready to serve, broil on low until the cheese is melted, bubbly, and lightly browned.

Finish the soup: Remove the bay leaf from the soup. Stir in the brandy if using. Taste and adjust seasoning with salt and pepper.

Serve: Ladle the hot soup into bowls. Place a slice of cheesy toast on top of each bowl and serve immediately. Enjoy with your half egg salad sandwich and a chilled glass of cucumber water.