Heat the oil in a large Dutch oven or heavy pot over medium-high heat. After 90 seconds when the oil is hot, add the mushrooms and pearl onions, and cook for 6-7 minutes, stirring occasionally, until lightly browned.
Add the garlic and carrots, and cook for 4 minutes, stirring occasionally, until the onions begin to soften and become fragrant.
Add the oregano, black pepper, rosemary, thyme, bay leaves, and tomato paste. Sauté for 3 minutes until the tomato sauce breaks down and the herbs are well incorporated.
Pour in the wine and lower the heat to medium. Simmer for 10 minutes, stirring occasionally, until the sauce reduces and the carrots are fork tender.
In a small bowl, whisk the cornstarch with the mushroom stock and tamari until smooth.
Add the starch and stock mixture to the pot. Stir well and cook for another 4-5 minutes until the sauce thickens.
Optionally, remove the rosemary sprigs, thyme sprigs, and bay leaves before serving. Garnish with parsley leaves or minced chives.