Wash and dry the greens; combine in a large salad bowl.
In a large, nonstick saute pan, cook the bacon over medium high heat until crispy; remove the cooked bacon from the pan, and drain on paper towels. Saute the mushrooms in the remaining bacon grease over medium high heat, seasoning with salt and pepper, to taste until mushrooms golden brown. Set cooked mushrooms aside on paper towels.
Add olive oil to the pan with remaining bacon grease, along with the shallots. Reduce heat to medium and saute the shallots until fragrant and translucent, about 2 minutes. Add in the garlic and thyme and cook for an additional minute, stirring constantly. Add in the vinegar and honey, then simmer for one minute.
Turn the heat up to medium high and pour in the beaten eggs. Season lightly with salt and pepper to taste and allow the eggs to simmer and cook for one minute before stirring. Cook the eggs until they are soft scrambled, only stirring the pan twice more. Add in the cooked bacon and stir once more. Pour the hot bacon egg mixture over the large bowl of winter salad greens. Season with salt and pepper to taste and gently toss. Serve immediately garnished with the cooked mushrooms.