Heat a large skillet over medium heat. Pour in 2 tablespoons of the olive oil and add the onion. Reduce the temperature to low and slowly caramelize the onion, cooking for 15 to 18 minutes. Add the garlic paste and cook for another 2 minutes. 

Add the mustard greens and cook until the greens have wilted. Increase the heat to medium, stir in the tomatoes, and cook for 3 to 5 minutes, until the moisture has evaporated. Remove from the heat and transfer the mixture to a medium bowl.

Fold the croutons into the mustard green mixture and season with the salt and pepper to taste. Cover and chill in the refrigerator for at least 30 minutes. 

Place the trout on a baking sheet, unfolding one side of each fish to open it like a book. Lightly season with salt and pepper. Now spoon about 3 tablespoons of the corn bread stuffing into each cavity. Make sure each fish has an even balance of corn bread, greens, tomatoes, and onion. Gently spread the stuffing the full length of the trout fillets; the depth of the stuffing should be about ½ inch. Fold the top half of the fish back over the stuffing. Transfer to the refrigerator to chill for 20 minutes. Preheat the oven to 200° F. 

Add the remaining 2 tablespoons olive oil to a large nonstick skillet set over high heat. When the oil is hot, add 3 trout and cook for 4 minutes on one side, then carefully flip the fish over and cook the second side for another 4 minutes, until a golden brown crust has formed and the flesh flakes and is opaque. Transfer the fish to a clean, lightly oiled baking sheet and place in the warm oven while the remain­ing fish cook. Repeat with the trout in 3 more batches, keeping them warm in the oven. 

To make the Hazelnut Brown Butter Sauce, pour off the oil from the skillet and return the pan to the stovetop. Add the butter and heat until it is a light golden color, about 2 minutes. Add the hazelnuts and cook until the butter develops a rich golden color, 1 to 2 minutes more. Remove the skillet from the heat and stir in the lemon juice and sage. Season with the salt and pepper to taste. 

Transfer the trout to the individual plates, spoon the Hazelnut Brown Butter Sauce over the top, and serve.

Cornbread croutons: Cut leftover cornbread into 1-inch chunks. Spread on a baking sheet and bake at 275 until crisp and golden, 20 to 25 minutes.