Heat olive oil in a saucepan or large skillet set over medium-high heat.
Add spinach to the heated oil and cook for 2 minutes, or until wilted, stirring frequently.I suggest cooking the spinach in 3 batches so it fits comfortably in the skillet, and cooks evenly. Use about a teaspoon of oil with each batch.
Remove from heat and transfer spinach to a cutting board; once it is cool enough to handle, chop up the spinach. Set aside.
Wipe down the saucepan.
Set saucepan over medium heat.
Add butter to the pan and melt it. Swirl around from time to time to melt nicely and prevent from browning.
To the melted butter add the onion and cook for 2 minutes, or until just softened.
Sprinkle flour over the onions; cook and whisk for 2 more minutes, or until lightly browned.
Add the milk in a slow stream while whisking; whisk until completely combined and the mixture begins to boil and slightly thicken.
Whisk in salt, pepper, paprika, and nutmeg.
Reduce heat to low and continue to cook for 5 minutes, whisking frequently.
Add the chopped spinach; stir to combine and continue to cook for 5 more minutes, stirring frequently, folding in the spinach as you stir. You want to mix and stir to completely combine the spinach with the sauce.
Remove from heat.
Taste for salt and pepper, and adjust accordingly.