Place rice flour in a medium bowl and season with salt and pepper. Mix eggs and milk in a large bowl and season with salt and pepper. Place cornmeal in a medium bowl and season with salt and pepper.
Preheat oven to 375 degrees F.
Open up and cut the trout, diagonally, into 2 fillets. Season both the flesh and skin sides of the fillet with salt and pepper, to taste, and then dip each fillet into rice flour, then egg mixture, then cornmeal. Repeat with remaining trout.
Heat 3 tablespoons of the oil in a large skillet until almost smoking. Saute 4 fillets at a time until golden brown on both sides. Repeat with the remaining oil. Transfer to a large baking sheet and repeat with the remaining 2 trout. Place in the oven and bake for 5 to 6 minutes until just cooked through.
Zest and juice both lemons, separately reserving the zest and the juice. Set aside.
While the trout is baking, melt the butter in a nonstick saute pan over medium-high heat. Watching carefully and lowering the heat if necessary, allow the butter to foam and turn golden brown. Immediately add the lemon juice, zest and salt and pepper, to taste.
While the butter is still foaming, add the pecans and parsley. Do not allow the butter to burn or it will be unusable.
Place 2 fillets on each of 4 dinner plates and pour the Pecan-Brown Butter over the top. Serve alongside the Sauteed Swiss Chard with Red Onion and Serrano Chile Vinegar.
Tear Swiss chard leaves from thick white stalks, discard the stalks and coarsely chop leaves, set aside.
Heat a large skillet over medium-high heat. Add the bacon and cook until golden brown and fat as rendered. Remove bacon to a plate with a slotted spoon. Add the onions and cook in the rendered fat until soft. Add the garlic and cook for an additional minute. Add the Swiss chard, season with salt and pepper and stir to coat the leaves in the fat. Cook until the leaves have completely wilted. Add the bacon back to the pan. Add the vinegar and continue cooking for 2 minutes. Serve with additional vinegar on the side.
Bring chiles, vinegar, and a teaspoon of salt to a boil in a medium nonreactive saucepan. Remove from heat, pour into a bowl, cover and let steep for at least 2 hours or overnight at room temperature. Strain through a fine strainer into a bowl or glass jar.