Peel and grate the potatoes and onion into a mixing bowl.

Add the egg, wheat flour, salt, and 1 tablespoon of olive oil; mix until evenly combined.

Heat 1 tablespoon of olive oil in a frying pan over medium heat.

Spread the potato mixture into one large flat rösti in the hot pan.

Cook the rösti for 15 minutes over medium heat, turning it occasionally until crisp and cooked through.

Halve the cherry tomatoes and finely chop the shallot on a cutting board.

Combine the tomatoes, shallot, basil, lemon juice, 1 tablespoon of olive oil, salt, and black pepper in a bowl.

Transfer the cooked rösti to a serving plate and top it with the cherry tomato salad.

Tear the burrata over the rösti and drizzle with the remaining olive oil.