For the chicken, heat a frying pan until medium-hot. Add the oil, half the butter and the chicken and fry until golden-brown and nearly cooked through (approximately 3-4 minutes).
Remove the chicken from the pan and set aside. Add the shallots to the pan and gently fry for 2-3 minutes until translucent. Increase the heat and add the pearl onions and mushrooms. Cook for 2-3 minutes until golden-brown.
Add the white wine and cook until reduced in volume by half, then add the stock and bring to the boil.
Cook for a couple of minutes, then add the chicken and return to the boil. Cook for two more minutes until the chicken is cooked through.
In a bowl, whisk the cream and egg yolks together. Add to the pan and stir through. Remove from the heat and season to taste with salt and freshly ground black pepper.
Finally, stir the tarragon through the sauce and keep warm until ready to serve.
For skinny fries, heat a deep fat fryer to 180C/350F. (CAUTION: Hot oil can be dangerous. Don't leave unattended).
Add the chips and fry for 4-5 minutes until golden-brown and cooked through.
Drain on kitchen paper then sprinkle with sea salt.
To serve, spoon the chicken onto the plate then pile the fries alongside.