Put the eggs in a small saucepan of water and bring to a boil over medium-high heat. Boil for 4 minutes. Turn off the heat and let cool in the water. When the eggs are cool, crack and peel them. Chop the eggs, season to taste with salt, and reserve.
Position a rack in the center of the oven and heat the oven to 375°F. Heat 1-1/2 Tbs. of the olive oil in a small saucepan over medium-high heat. Add the garlic and cook, stirring occasionally, until it starts to turn gold, about 1 minute. Discard the garlic.
Arrange the bread in a single layer on a baking sheet. Drizzle with the garlic-infused oil, sprinkle with a little salt, and toss. Bake, shaking the bread cubes once, until golden and crispy, 8 to 10 minutes. Remove from the oven and let cool.
In a small bowl, whisk together the remaining 3 Tbs. olive oil, the sherry vinegar, and the mustard. Season with salt and pepper to taste.
In a 10-inch skillet, cook the bacon over medium-high heat, stirring frequently, until golden brown and crisp, 3 to 5 minutes. With a slotted spoon, transfer the bacon to a plate lined with paper towels. Add the shallot to the pan and cook, stirring, until softened, about 1 minute. Let the pan cool slightly and add the vinaigrette to the pan, whisking well to blend the ingredients.
Toss the warm vinaigrette and the spinach together in a large bowl. Transfer to a platter and garnish with the chopped eggs, bacon, and croutons. Serve immediately.