Crisp Petrale Sole with Browned Butter Sauce and Carrot Flan

Before preparing the sole, make the carrot flans and hold them in warm oven. Set up a pot of boiling salted water with a tablespoon of butter to blanch some tender pea vines when you are ready to plate the sole.  Prepare the sole fillets just 2 at a time so as not to crowd the pan. Hold them, as they are prepared in the warm oven.   

(For each serving)

For the Sole:

One 6-ounce petrale sole fillet

kosher salt and freshly ground black pepper
flour in a wide shallow dish or hotel pan

1 tablespoon butter

1 tablespoon canola oil

For the Browned Butter Sauce

1 tablespoon butter
2 teaspoons freshly squeezed lemon juice

1 tablespoon chopped parsley
lemon wedge for garnish
For the Pea Vines Garnish
1 quart boiling water
1 tablespoon salt
1 tablespoon butter
12 ounces tender young pea vines

1.) Pat the fish dry with paper towels and sprinkle it with salt and pepper. Coat both sides of the filet in flour, shake off the excess and lay the filet on a sheet of parchment.
2.) Heat a sauté pan over medium-high heat with the butter and canola oil and swirl to melt the butter. Carefully lay the floured filet in the pan and cook until the edges of the filet are opaque and the underside is golden brown, about 3 minutes. With a fish spatula, gently turn the filet and cook until the filet is cooked through, about 2 minutes longer. Transfer the filet to a heated dinner plate and invert one of the carrot flans onto each plate.
3.) Transfer the sole to a heated dinner plate and hold in a warm oven while you make the browned butter sauce. Wipe out the pan with a paper towel and add the fresh tablespoon of butter. Cook until the butter is golden brown and has a nutty aroma. Swirl in the lemon juice and parsley and transfer the sauce at once to the plated fish. Garnish with a lemon wedge and serve.
4.) To prepare the pea vines, plunge them into the boiling salted water with the butter and transfer them to the plates.