1. Sauté garlic and shallots in the olive oil on medium for just a few moments, then add the fennel and cook about 1 minute more
2. Add wine, stir a few moments, then add the broth, dill, and mushrooms. I put about a little less than equal the amount of fennel. Season with salt and pepper.
3. Cover, and cook on medium-low heat for up to 30 minutes, stirring occasionally. If you think the liquid is getting too low for the sauté, just add a little splash more water.
4. Cook until the fennel is very soft, and the liquid has reduced out, it should be starting to almost caramelize, and will be almost sweet.