Fry the lardons in half the olive oil until crisp and then set aside.
In the same pan, add a little more oil and fry the potatoes, set aside with the lardons in a warm place.
In a bowl, combine the mustard with the extra virgin olive oil, walnut oil and red wine vinegar.
In the frying pan, heat the remaining olive oil and cook the pigeon breasts with the garlic and thyme, turning and seasoning as they cook. The breasts don t take long, 2-3 minutes each side maximum. Cover and allow to rest.
Combine the salad leaves, ¾ of the dressing, lardons, potatoes and seasoning in a large bowl and serve on four large plates.
Cut the pigeon breasts into thin slices and arrange over the salad. Sprinkle over some sea salt and the remainder of the dressing. Serve immediately.