Heat olive oil in a saucepan or large skillet set over medium-high heat.
Add the spinach to the heated oil and cook for 2 minutes or until wilted, stirring frequently. Remove from heat and transfer the spinach to a cutting board; once it is cool enough to handle, chop it up. Set aside.
Wipe down the saucepan and set it 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 the 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 to the pan, 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 combine the spinach with the sauce completely.
Remove from heat. Taste for salt and pepper, and adjust accordingly.
Serve.