Hi,
I’m just trying to decipher what exactly you’re trying to do. When you say “double batch”, are you doubling a 5-gallon batch to 10-gallon? I’m assuming so since it sounds like you’re brewing extract with steeping grains. And you’re planning a partial boil, right?
My initial thought is that I’d just brew two different extract kits of the same recipe. One this week, one next week. Keep it simple. It would consume double the time, but is a sure-fire way to make sure you get 10 gallons of the intended recipe.
But if you want to do it all in one brew, then I’d imagine you could double up on everything. Put all the specialty grains from both kits into one grain bag, steep in double the amount of water than normal for 20 minutes or until you reach 170, then double up on all the boil additions at the normal times. And yeah, I agree, after chilling I would top up in the kettle and then split it evenly between two carboys, pitching equal amounts of yeast into both. But I suppose you could also just split the wort evenly between both carboys and then top up to 5 gallons in each…
Please don’t take my word for it, though. I’ve never scaled extract recipes before. Only all grain. And I have software that does it for me. Do you have any brewing software? I recommend plugging the double batch ingredients into some software, specifying your boil size and total yield, and then seeing if the numbers line up (OG, IBU, SRM, etc.) to the original 5-gallon recipe. I use brewersfriend.com for this. You can use it for free and save up to 5 recipes if you don’t want to pay for a subscription.
Hope this helps