Blanch the chips in a pan of salted boiling water, for 4-5 minutes, or until just tender. Drain.
Half-fill a deep, heavy-based saucepan or a deep fat fryer with veg oil and heat to 140C/284F (use a digital thermometer to check this). Fry the chips for 8-10 minutes, or until the oil stops bubbling, which means that the moisture has been removed. Remove the chips from the oil and set aside to drain on kitchen paper.
Heat the oil to 180C/350F (use a digital thermometer to check this) and fry the chips for 4-5 minutes, or until crisp and golden-brown. Remove the chips from the oil, set aside to drain on kitchen paper and season to taste with salt.
For the onion rings:
Slice the onion into rings. Mix together the seasoned flour, water and trisol to make a batter consistency then dip in the onion and deep until golden and crispy
For the béarnaise:
Combine the wine vinegar, 2tbsp snipped tarragon, the shallot and peppercorns in a small, heavy-based saucepan and reduce by half over a low heat. Set aside to cool.
When the vinegar reduction is cold, add the egg yolks and 3tbsp cold water. Set the pan over a low heat and whisk continuously, making sure that the whisk reaches right down into the bottom of the pan. As you whisk, gently increase the heat; the sauce should emulsify slowly and gradually, becoming oily after 8-10 mins. (Do not let it become hotter than 65ºC.)
Turn off the heat and whisk the clarified butter into the sauce, a little at a time.
Season with salt and pepper and pass the sauce through a conical sieve into another pan. Stir in the rest of the tarragon, the chervil and lemon juice. Check the seasoning and serve at once