Rinse and pat dry meat. Peel and quarter onion. Peel and rinse carrot and celery, cut into pieces. Combine white wine and water, season with salt and bring to a boil. Add meat and vegetables to the pot and cook on low heat for 1 ½ hours.
Combine egg yolks with ¾ of oil and lemon juice, season with salt and whisk until creamy mayonnaise results. Combine 1 tablespoon of capers, anchovies and tuna in a blender, mix in remaining oil and puree. Strain tuna mixture through a sieve and mix with mayonnaise.
Remove meat from the pot and cool, slice and arrange on plates. Drizzle with tuna sauce and sprinkle with remaining capers, garnish with watercress and lemon slices. Serve.