Preheat the oven to 350°. Bring a small saucepan of water to a boil. Add the egg and cook for 5 minutes, until soft-boiled. Remove the egg with a slotted spoon and crack it into a blender, using a small spoon to scoop out all of the egg yolk and white. Add the anchovies, lemon juice, whole garlic clove and mustard and blend until smooth. With the machine on, add 1/4 cup plus 2 tablespoons of the olive oil in a thin stream. Add two thirds of the finely grated Parmesan and season with salt and pepper.
In a large bowl, toss the baguette cubes with the remaining 3 tablespoons of olive oil. Add the remaining finely grated Parmesan along with the paprika and minced garlic and toss to coat. Spread the bread cubes on a rimmed baking sheet and toast for about 8 minutes, until crisp and golden. Let cool slightly.
In the same large bowl, toss the spinach with the dressing, croutons and the shredded Parmesan; season with salt and pepper. Transfer the salad to plates and serve.