Start by preparing the dressing. Cut the yellow tomato in half, then grate it flesh side down on a grater with large holes, keeping the skin in your hand. Pour the pulp into a bowl.
Add the olive oil, lemon juice, balsamic vinegar, grated garlic, oregano, salt and pepper. Mix briskly. The sauce should be juicy, fragrant, slightly tart and well seasoned by the garlic and oregano.
Take two or three spoonfuls of this grated tomato dressing and mix them with the crumbled roast chicken. Let rest while you prepare the rest of the salad.
Cut off the tough base of the asparagus. Fry them in a large skillet with a drizzle of olive oil, salt and pepper for 6 to 8 minutes, until tender but still slightly crunchy. They should be golden in places. Let them cool for a few minutes.
Meanwhile, cut the second yellow tomato into thin slices and arrange them in a large serving dish, such as a carpaccio. Lightly salt the tomatoes to bring out their juices.
Toast the slices of bread. Rub them while still hot with a clove of garlic cut in half, then drizzle them with olive oil. Set aside.
Add the grilled asparagus on top of the tomatoes, then spread the marinated chicken on top. Tear the burrata into pieces and place them in the dish. Add the coarsely chopped green olives.
Drizzle with the remaining grated tomato dressing. Finish with the chopped chives, a few mint or parsley leaves if desired, a turn of black pepper and a final drizzle of olive oil.
Serve immediately with the garlic toast, to be dipped in tomato juice, olive oil and burrata.