Preheat the oven to 425°F. Rinse the trout and pat dry inside and outside. Scrub the potatoes and cut into thick slices. If the potatoes are large, cut in half before slicing. Finely chop the fresh parsley, dill, and chives, setting aside a few sprigs of each for the trout. Mince the garlic. Thinly slice half of one lemon, cutting the slices in half into half-moons.
Heat 1 tablespoon each of the olive oil and butter in a large non-stick skillet over medium low heat. Add the potatoes and season with a sprinkle of kosher salt. Cover the potatoes and allow to cook until they are almost fully cooked. Toss the potatoes every couple of minutes so that they cook evenly. The potatoes should take about 15 minutes to cook through. Add a bit more olive oil if needed to prevent the potatoes from sticking.
Spray a baking sheet with non-stick spray, or line with parchment paper. Season both the outside and inside cavity of the trout generously with kosher salt and pepper. Stuff the cavity of each trout with a few sprigs each of the parsley, dill, and chives. Add a couple slices of lemon along with a few slivers of butter.
Transfer the trout to the prepared baking sheet. Top each trout with a few slivers of butter and the remaining lemon slices. Bake the trout for 10 to 15 minutes until it reaches an internal temp of 145°F.
When the potatoes are almost done, remove the lid and turn the heat up to high. Continue cooking, tossing regularly, until the potatoes are golden brown and fully cooked. Turn the heat down and push the potatoes to one side of the skillet. Add the remaining tablespoon of butter along with the minced garlic. Sauté the garlic briefly until fragrant and then toss with the potatoes.
Generously sprinkle the potatoes with the chopped parsley, dill, and chives and season with kosher salt and pepper to taste. Lastly, squeeze the juice of one lemon over the potatoes and toss again.
To serve, remove the lemon slices and herb filling from the trout and arrange on a platter. Garnish with extra chopped herbs and squeeze over the remaining half lemon if desired. Serve with the new potatoes and enjoy!