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1. Peel and chop the onion, leeks and celery. Peel and slice the carrots. Place onion in the bowl fitted with the ultrablade knife. Mince at speed 11 for 10 seconds.
2. Replace the ultrablade knife with the mixer. Add olive oil, celery, white wine and broth. Launch the P1 simmer program at 270°F for 5 minutes.
3. At the end of the program, add boneless skinless chicken thighs, carrots, leeks, bay leaf and thyme. Season with salt. Launch the P2 simmer program at 200°F for 45 minutes.
4. At the end of the program, drain the meat and vegetables and place in a large bowl. Add cream mixed with the egg yolk into the remaining juice. Mix at speed 6 at 160°F for 2 minutes. Pour sauce over the meat and vegetables. Divide the chicken thighs, vegetables and sauce among 4 soup bowls. Serve immediately.