OK. Hold up. We need to clarify what we're talkin' about here.
11# of Pilsner Malt is indeed a grain, it is a base grain. There's not really "steeping" with base grains. If you want to use extract, I would just use Pilsen Light DME or Xtra Light DME, and if possible, do a late addition for about 2/3 of it. (Make sure to calc your hops correctly if you do a late addition.)
What you are used to steeping are specialty grains, for the most part, and their job is to add colors and flavors to the wort. In the case of a Belgian Golden Strong, there AREN'T really any colors or flavors to add -- because the yeast is responsible for most of the flavor!
You could, theoretically, ferment the entire time at 64˚F, but you *might* see a stuck fermentation, and you will probably miss out on some of the yeast-caused esters, which really "make" a BGSA what it is. Are there any warmer rooms in the house that, after 2-3 days of fermentation, you could move the fermenter to for a while? Or can you just raise the thermostat a bit, and deal with a warm house for a few days towards the end of your fermentation?
Finally: Sparging. To make it as simple as possible....
- Mashing, as you know, is one big steep, with a carefully calculated amount of water (that determines your mash thickness) at a certain temperature (that determines your wort's fermentability and flavor profile).
- Once starch conversion is complete, and you are done with your mash, you drain the sweet wort out of the mash tun. But a number of sugars are still stuck in the grain bed, so sparging basically just rinses those sugars out of the grain -- but in a controlled manner.
- There are two kinds of sparging, batch and fly, and they work in slightly different ways.
(Past here, John Palmer's How To Brew and other sources, like the HBT wiki, should be able to fill in all the details. )