Preheat the oven to 200 degrees Celsius.

Bring a large quantity of water to a boil in two saucepans.

Prepare the vegetable stock.

Mince the shallot, chop the parsley, and halve the cherry tomatoes.

Squeeze the lemon and mince or crush the garlic.

Cut 2 cm from the ends of the green asparagus.

Cook the asparagus for 1 to 2 minutes in one of the saucepans, then plunge into cold water.

Combine cherry tomatoes, black balsamic vinegar, brown sugar, garlic, and olive oil in a baking dish.

Season with salt and pepper, then bake for 20 to 25 minutes.

Cook the linguine for 8 to 10 minutes, covered, in the other saucepan. Drain and set aside.

Flatten the chicken fillet using parchment paper or cling film.

Season the chicken with salt and pepper.

Heat half a tablespoon of butter per person in a sauté pan over medium-high heat and cook the chicken for 3 to 4 minutes per side.

Wrap the chicken in aluminum foil to keep warm while preparing the sauce.

In the same pan, cook shallots for 1 to 2 minutes, then add lemon juice, vegetable stock, and capers. Let it reduce for 3 to 4 minutes.

Off the heat, stir in butter, then add cherry tomatoes and half of the parsley.

Gently incorporate linguine, then season with salt and pepper.

Serve the linguine on plates, arrange the green asparagus alongside, and place the chicken on top. Garnish with remaining parsley.