Wrap the entrecote in the hay and put in a vacuum bag. Cook in water for 1 hour at 53 °C. Remove the meat from the vacuum bag and clean off the hay. Season the meat with salt and pepper. Fry briefly in hot olive oil.
Braise the onion in the olive oil with the thyme. Add the Yellow pepper purée and let boil for 1 minute. Blend and strain. Thicken the sauce with cornstarch. Weigh 75 g of the made purée. Add the egg white and blend. Add the olive oil slowly. Season this mayonnaise to taste. Place at least 30 minutes in the refrigerator before use.
Just before serving, sprinkle some ground coffee on top of the mayonnaise.
Halve the cherry tomatoes. Season with salt and pepper. Place on a baking tray, drizzle with some olive oil and lay a sprig of thyme on the tomatoes. Roast the tomatoes in a preheated oven at 180 °C.