Remove the stems from the spinach and wash, drain, and pat dry thoroughly. Place into a large mixing bowl and set aside.
Place the eggs into an electric kettle and cover with cold water by at least 1 inch. Turn the kettle on. Once the water comes to a boil, the kettle will turn itself off. Leave the eggs in the water for 15 minutes. Remove and peel off the shell. Slice each egg into 8 pieces and set aside.
While the eggs are cooking, fry the bacon and remove to a paper towel to drain, reserving 3 tablespoons of the rendered fat. Crumble the bacon and set aside.
Transfer the fat to a small saucepan set over low heat and whisk in the red wine vinegar, sugar, and Dijon mustard. Season with a small pinch each of kosher salt and black pepper. For a creamy dressing, remove the cooked yolks from the eggs and put them in a large mixing bowl. Mash with a fork. Whisking continuously, add the vinegar, sugar, mustard, and melted bacon fat until an emulsion is formed. Season with a pinch each of salt and pepper.
Add the mushrooms and the sliced onion to the spinach and toss. Add the dressing and bacon and toss to combine. Divide the spinach between 4 plates or bowls and evenly divide the egg among them. Season with pepper, as desired. Serve immediately.