Pre-heat the oven (or air fryer) to 400˚F.

Bring a small saucepan of salted water to a boil. Blanch the potato slices for 2 minutes, until they just start to soften slightly. Drain and dry with a clean kitchen towel.

Cut out 2 large rectangles of parchment paper – about 13-inches by 15-inches each. Toss the potatoes, fennel, half of the melted butter, salt and freshly ground black pepper together in a bowl. Divide the vegetables between the two pieces of parchment paper, placing the vegetables on one half of each rectangle. Sprinkle some fresh dill on top.

Place a fillet of salmon on each pile of vegetables. Season the fish very well with salt and pepper. Toss the cherry tomatoes on top. Drizzle the remaining butter over the fish. Divide the vermouth between the two packages, drizzling it over the fish.

Fold up each parchment square by first folding the rectangles in half over the fish. Starting at one corner, make a series of straight folds on the outer rim of the squares to seal the edge together.

Place the two packages onto a baking sheet and bake in the 400ºF oven for 15 to 20 minutes. (or, cook one package at a time in the air fryer for 10 minutes each.) The package should be puffed up and slightly browned when fully cooked. The fish should feel firm to the touch (you can often, carefully, press on the fish through the paper).

You can serve these simply with the parchment paper already cut open to reveal the insides, have your guests cut open the packages at the table, or remove the parchment completely, transferring the tasty insides to a plate. Garnish with a little more fresh dill.