Heat the oil in a small frying pan over medium heat. Add the shallots and cook, without browning, until soft. Add the mushrooms, season with salt, and continue cooking until all the water is released from the mushrooms and evaporated.
Stir in the cream and cook until reduced. Add 35 grams of the cheese to the mixture and stir until the cheese is melted and combined. Set the mixture aside to cool.
Bring a saucepan of water to boil over high heat. Trim the zucchini and blanch for about 4 minutes. Chill the zucchini in an ice bath. Cut the zucchini in half lengthwise and scoop out the centers.
Fill the scooped-out zucchini halves with the mushroom mixture. Tightly wrap each filled half in plastic wrap and refrigerate until needed.
Preheat the oven to 430ºF.
Unwrap the zucchini halves and place them on a baking sheet. Sprinkle with the remaining cheese. Bake until tender, about 25 minutes. Allow the zucchini halves to rest a few minutes before serving.