Heat a saute pan glazed with the olive oil over medium-high heat. Add the bacon pieces and saute them until they develop a crispy exterior but remain tender on the inside, adjusting the heat as necessary, 5 to 10 minutes. Remove about 1 teaspoon of the bacon fat and reserve on the side. Add the shallots to the pan and saute until soft, another minute or 2. Add the mushrooms, and once they begin to soften, after about 2 minutes, add the stock, scraping the browned bits from the bottom of the pan as the liquid comes to a boil.
Reduce the pan liquid by half. Add the balsamic vinegar, bring to a simmer and then remove the pan from the heat. Taste the pan sauce looking for a proper balance of fat and acidity. If the sauce tastes too fatty, add another dash of balsamic. If it's too acidic, correct it with additional extra-virgin olive oil. Heat a large nonstick pan over medium-low heat.
Glaze the pan with the reserved bacon fat and crack in the egg, taking care not to break the yolk. Sprinkle the egg with a pinch of salt and some black pepper. Fry the egg gently until the white is cooked through but the yolk remains runny.
Place the spinach in a large bowl. Pour the warm dressing, with the bacon and mushrooms, over the spinach and toss until the leaves are wilted and coated. Top the salad with the fried egg and cut it into bite-size pieces as you toss the salad, incorporating the yolk into the dressing. Divide the spinach salad among 4 plates and serve.