1 tablespoon olive oil, coconut oil, or butter
1 medium carrot, large dice
1 medium leek, halved lengthwise, rinsed, and sliced crosswise into 1-inch pieces (white and pale green parts only)
1 medium yellow onion, large dice
6 medium garlic cloves
2 pounds medium white button mushrooms, stems trimmed and quartered
8 Italian parsley sprigs
6 thyme sprigs
1 bay leaf
2 teaspoons whole black peppercorns
3 quarts (12 cups) water
1/4 teaspoon kosher salt
Heat the oil in a large pot over medium-high heat until shimmering. Add the carrot, leek, and onion and cook, stirring occasionally, until the onions and leeks have softened, about 8 minutes. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute.
Add the mushrooms, parsley, thyme, bay leaf, and peppercorns and cook, stirring occasionally, until the mushrooms start to release some moisture, about 4 minutes.
Add the water and bring to a boil. Reduce the heat to low and simmer until the vegetables are completely soft and the stock has a pronounced mushroom flavor, about 1 hour.
Remove from the heat and strain through a fine-mesh strainer set over a large heatproof container or saucepan; discard the contents of the strainer. Stir in the salt. If not using immediately, let cool to room temperature, then refrigerate for up to 3 days or freeze for up to 1 month.