Prepare the ingredients as listed.
Combine the water and cucumber slices. Refrigerate to infuse.
Bring a pot of salted water to a boil, add the potatoes, and cook until fork-tender. Drain and set aside.
Heat the olive oil in a skillet over medium heat. Add the garlic and onion and sauté until softened.
Add the ground beef and cook, breaking it up, until browned. Stir in the flour and cook briefly.
Add the beef broth, corn, peas, ground sage, and fresh thyme. Season with salt and black pepper to taste and simmer until thickened.
Preheat the oven broiler.
Melt the butter and stir in the heavy cream. Mash the potatoes, gradually incorporating the butter and cream mixture, and season with salt and black pepper to taste.
Transfer the beef mixture to an oven-safe dish and spread the mashed potatoes evenly on top.
Broil until the potato topping is lightly golden.
Serve the shepherd’s pie with cucumber water.