Place the egg in a small saucepan and cover with cold water. Bring to a boil, then cover, remove from heat, and let sit for 9 minutes before transferring to an ice bath; peel and quarter.
Drain the canned tuna thoroughly and place it in a large mixing bowl, flaking it into bite-sized pieces with a fork.
Dice the cucumber into small cubes and halve the cherry tomatoes.
Use a vegetable peeler to create thin ribbons of zucchini and finely shred the carrots.
Add the cucumber, tomatoes, zucchini ribbons, and shredded carrots to the bowl with the tuna.
In a small jar or bowl, whisk together the extra virgin olive oil, lemon juice, sea salt, black pepper, and dried oregano to create the dressing.
Drizzle the dressing over the tuna and vegetable mixture, tossing gently until everything is evenly coated.
Crumble the feta cheese over the salad and top with the quartered hard-boiled egg.
Toast the slice of integral bread until golden and crisp, then serve immediately alongside the salad.