Preheat the broiler, first raising a rack to the highest position in the oven.
In the bowl of a mortar and pestle, mash and grind the garlic clove. When the oils have covered the walls of the mortar, remove and discard the garlic flesh. Add the almonds to the bowl and grind until they are broken up into smaller pieces. Add the dandelion greens and lemon zest and mash all the ingredients together until combined. The mixture will look a little bit like a salad and a little bit like a pesto. Inconsistency in the size of the leafy bits is perfect. Add the olive oil and a pinch of salt and give it one last stir with the pestle. Set aside.
Meanwhile, season the trout on both sides and inside the belly with salt and pepper. Insert several lemon slices into the belly of the trout. Place on a sheet pan and lightly coat the trout with a drizzle of olive oil to prevent sticking. Place the sheet pan directly under the broiler, and broil on one side until the skin starts to shrivel and char, 4-5 minutes. Take out the pan and flip the trout with a spatula. Return to the broiler and broil the other side until charred and cooked through, 4-5 minutes.
Place the broiled trout on a platter and spoon the dandelion salad over it. Serve immediately.