Preheat oven safe skillet over high heat or wrap rubber handles in double layers of foil to protect the surface in the oven.
Prick the potatoes 3 or 4 times each with a fork and cook them in the microwave on high for 5 minutes.
Pat cod dry and squeeze a little lemon juice over it and season with salt. Drizzle fish with extra-virgin olive oil.
When potatoes cool just enough to handle, slice them into 1/4-inch pieces lengthwise. Coat them with extra-virgin olive oil and salt and pepper. Arrange them on a cookie sheet in a single layer and roast them for 20 minutes. Do not move them or turn them as they cook. Chop tarragon, chives and parsley and combine and reserve.
Add cod seasoned side down to very hot skillet. Sear it 2 minutes, then drizzle the tomatoes with extra-virgin olive oil and season them with salt and pepper and add them to the fish. Sear tomatoes 1 minute, then transfer the pan to the oven and roast the fish and tomatoes 8 minutes until fish if firm and opaque and tomatoes have all burst.
Place parsley, mint, chicken stock and shallot in food processor or blender and puree. Transfer to small sauce pot and bring to a simmer. Season the broth with salt and pepper, to your taste.
Heat the light frying oil in small skillet over medium heat. Add sliced garlic to the hot oil and let it fry until crisp and golden brown, 3 to 5 minutes. Drain garlic chips on a paper towel and reserve.
When the potatoes are very brown and crisp on the bottom side and tender on the top side, remove. Coat sliced potatoes liberally with the chopped herbs.
Pour warm pesto broth onto each dinner plate.
Remove the fish from the oven. The bottom should be crisp and brown. Turn the fish over to place the crispy side up in pools of parsley-mint broth. Arrange the herb potato slices and tomatoes decoratively around the fish. Top the dish off with a scattering of garlic crisps and serve. (You could get $40 a head for this plate! Nice!)
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