I've seen a very good instructional video for a 1 gal extract brew on the Basic Brewing website. I've also read somewhere (possibly on here?) that some have reportedly brewed by the pint. The point is, there's technically no minimum brew size. The main thing would be that you have equipment that matches the size of your brew.
I regularly boil 2.5 gallons of water for a 5 gallon recipe. The kit is designed for a 2.5 gallon boil. The hop schedule is also designed for a 2.5 gallon boil.
Hop utilization is less as the SG of the wort increases. If I were to boil 2 gallons hop utilization would be less because this would increase the SG. Boiling 3 gallons would increase hop utilization because the SG of the wort would be decreased.
The difference in hop bitterness and aroma may not be noticeable with a 0.5 gallon increase or decrease in boil volume. I'm sure a 1 gallon boil would make a noticeable difference.
If I had the capability to boil 5 gallons I would for the increased hop character without the cost of additional hops. Would this throw off the balance between bitterness and aroma. I don't know.
I brewed a coopers canadian can, used all malt and filled to 19L than dry hopped with 1oz crystal hops, bottle carbonated and it turned out great with a citrus taste to it, my non homebrew drinking friends liked it a lot, great head retention too, frothy the entire way down the glass.....although couldn't tell you what 15L batch would taste like, I would imagine you would taste a little more hop flavouring that is in the can
As mentioned, there technically is no minimum about you can brew. 1 gallon brewing is common and is a great way to make a wide variety of beers and to try out new recipes before upscaling the quantity. I personally wouldn't brew less than 1-2 gallons. With the amount of time an effort it takes I would like a decent amount of beer at the end. Even if it's not great beer, it's still beer.
Sure, 1 gallon of beer would take less time to make than 5 gallons, but not 1/5 of the time.
Also when brewing small quantities I suspect you need to be more careful about OVERpitching the yeast.
Well I made an ipa 2 weeks ago and it by far was the most violent brew I have ever made, with in about a day it was foaming up through the lid and pouring onto the floor, I also notice that although the ambient temperature was 22 Celsius the temperature inside the bucket rose to about 27 Celsius until it slowed down the fermentation only about 2 to 3 days in. Never seen this before but it appeared to me that the yeast was doing its magic at such an alarming rate it actually was heating up the wort. Have not tried it yet as it is still in my secondary. But I would wonder if over pitching would have the same effect.
I have done about a dozen batches and this is the first time this has ever happened, I also used a Brew House kit that I bought out of my area and thought I would try for fun, I usually do coopers cans, although the Brew House kit came with coopers yeast so yeast wise it was nothing out of the ordinary