Preheat the oven to 400 degrees F. Line a rimmed sheet pan with parchment paper.
Place the mushrooms, shallots, oil, thyme and salt in a bowl. Toss to coat the vegetables evenly. Spread the mixture evenly on the lined sheet pan.
Bake until the shallots are lightly browned, about 35 minutes. Allow to cool slightly. Place half the cooked mushroom mixture in a blender using tongs and add half the chicken broth and sour cream. Blitz until smooth and transfer to a large soup pot. Repeat with the remaining mushroom mixture, broth and sour cream.
To serve immediately, warm the soup through and season with salt and pepper to taste.
To freeze, divide the soup evenly among four 16-ounce mason jars. Leave at least 1 inch of space at the top of each jar to prevent cracking. Screw on lids and freeze. To serve, place jars in a saucepan filled with cold water over medium heat until warm. Or, place a frozen jar in your lunchbox and reheat in the microwave for an on-the-go lunch.