Either one at a time, or in two separate saucepans, brown the onions and celery separately in about 1 tablespoon of the butter each. (Over the years we've determined it's much easier not to brown them together- it takes way longer and they don't brown at the same rate.)
When brown, transfer the onion and celery into a large mixing bowl and set aside to cool slightly.
Trim the crusts of the bread (I've made it before not trimming the crusts and while it's still good, I like the crust-free texture better.) and cut it into cubes. Transfer cubes into the same bowl as the onions/celery.
Melt the remaining butter and pour it into the bowl along with the broth, parsley and paprika. Mix together with your hands thoroughly.
Add the salt- one tablespoon first, and then taste the mixture to see how much more you need. (If you are using extremely salty broth you may need a little less. I usually use the whole amount.)
Spread stuffing into a 9x13 or other similar sized baking dish. If the pan is too packed in the center it will be difficult to heat, so I like to made the middle of the dish a little bit scooped out so it bakes for less time.
At this point the stuffing can be covered air-tight and stored in the fridge overnight until you're ready to bake it and serve. When that time comes- bake at 375 for 30-45 minutes, depending on the thickness of the pan. It is done when the top is crisp and the inside is hot.
*You don't want to use something flimsy like Wonderbread for this or the bread will disintegrate with all the liquid. Any heartier white sandwich bread will do- I like the kind called "Country White"
**Old Bay Seasoning is a wonderful sub for Paprika- I may even like it better if I'm willing to stray from the original recipe.
***I used to just add the full 2T of salt every time I made this, but this last time I used a new type of salt that happened to be "saltier" it made the result a little salty, so now I recommend adding it gradually and tasting to see how much you need.