Blanch the shallots in boiling water for about 5 minutes.
Drain and peel the skins off the shallots.
Heat 2 tablespoons oil in a skillet until hot.
Add the shallots and carrots, and when the vegetables are a little brown and starting to get tender, add the garlic and cook for another minute.
Transfer the vegetables to a 4- to 6-quart slow cooker (sprayed with Pam).
Add all the remaining ingredients except the mushrooms.
Stir and cook in the slow cooker on low for 6-8 hours.
Sauté the mushrooms in the skillet with 2 tablespoons olive oil until they are soft and turning brown. As Julia Child said, "The secret to good mushrooms is: don't crowd the mushrooms."
Set the mushrooms aside; stir mushrooms into the stew about 20 minutes before you plan to serve the stew.
Serve with cornbread or crusty French bread and a glass of red wine.