At least 3 to 6 hours before serving
Preheat a water bath to 140°F (60°C).
Trim any silverskin from the pork tenderloin. Mix together the spices in a bowl. Salt the pork tenderloin then sprinkle with the spice mixture. Place the pork in a sous vide bag then seal. Cook the pork tenderloin for 3 to 6 hours. For more information about the cooking range you can read my detailed article about why is there a range in sous vide cooking times.
At least 20 minutes before serving
Heat the oil over medium heat then add the shallot and garlic. Cook until the shallot is translucent, about 5 minutes. Add the mushrooms then cook, stirring occasionally, until the mushrooms are tender and browned. Stir in the butter until it melts then salt and pepper to taste. Remove from the heat.
At least 10 minutes before serving
Heat the oil over medium to medium high heat. Add the snow peas in a single layer, working in batches if necessary. Let the snow peas cook until they just start to brown and bubble, then flip them. Once the other side browns remove them from the heat and set aside.
10 minutes before serving
Blend or whisk together the water, yellow mustard, and soy lecithin then pour into a wide, flat-bottomed container. It can stay at this stage for a few hours.
First, make the mustard air sauce by running the immersion blender or Aerolatte milk frother in the mustard-water mixture. Try to keep the blender halfway out of the liquid so the air is more easily incorporated. This can sometimes take several minutes and there will still be liquid left at the bottom of the bowl. Once there is a decent amount of foam on top, let it sit for 1 minute to stabilize.
Remove the cooked pork tenderloin from the sous vide bag and pat dry. Lightly salt and oil the outside of the pork then quickly sear it until it is just browned. Slice the tenderloin into 1/2" to 1" pieces (12 to 25 mm).
Place the fried snow peas on a plate and top with a few slices of the sous vide pork tenderloin. Place some chanterelle mushrooms around the sides. Drizzle with olive oil and sprinkle with salt. Top with the mustard air right before serving.