My first attempt at brewing, bottled last week, was actually a mint ginger ale. Here's the procedure I used. I wrote this down incase I wanted to make it again.
Minger Ale
Ingredients
4-5 gallons water Preferably filtered
12 tablespoons spearmint tea
4 large tea bags
4 short pieces of string
6 grams munton premium gold active brewing yeast
1 1/2 cups lime juice
11 1/4 cups ginger syrup, see directions for making below.
5 cups baking splenda
1/2 lb fresh ginger root.
2 lbs of sugar, approximent
Pour 3 gallons of water into a large slow cooker or stock pot. Bring the water to a bare simmer. Spoon 3 tablespoons into each of the tea bags. Close up the tea bags, place the tea bags in the simmering water. Simmer for 7-15 minutes to taste. Remove tea bags. Remove from heat. It is also fine to add the tea earlier, it just won't do much until the water is hot.
Grate the ginger root into a medium sauce pan. It is not necessary to peel the ginger first. Cover with more of the water. Boil until the ginger smell mellows. This can take anywhere from 10 minutes for new ginger, or around an hour for old ginger.
Pour the contents of the pot through a sieve into a bowl. Make sure to get all the ginger out of the pan. Discard the ginger solids in the sieve.
Use a 1 cup measuring cup to move the liquid from the bowl back to the sauce pan. Make sure to keep track of how much liquid you have. Add 1 1/2 times the volume of the liquid, in sugar, to the sauce pan. Keep on low-medium heat, stirring regularly, until the sugar has dissolved. Remove from heat.
Place remaining water in a pot or sauce pan and bring to a boil. Remove from heat. Cover.
Allow the syrup, tea, and water to cool.
Using a funnel, pour the 11 1/4 cups syrup into a sterilized 4+ gallon bottle or carboy. Add the yeast, lime juice, tea, and splenda. Add additional water until you reach a volume of 4 gallons. Place the cap on the bottle, shake to combine and aerate. Install your airlock. Place the brew someplace cool and dark. Wait...
The reason I used spearmint is both that it isn't "peppery" the way pepper mint is, and it grows wild in my backyard. I cut it every 2-3 weeks and it produces 1 1/2 to 2 cups of dried peppermint each time. This is after destemming and crumbling into tea sized flakes.
The overall flavor is good. Strong mint flavor. Good ginger flavor too. The boiling mellows the ginger considerably. Not much fire, just good flavor. A little warmth in the back of the mouth after drinking is all. The color is a light yellow with a tinge of green to it. It was practically opaque when I bottled and pasturized it. It is still slightly murky after chilling in my fridge for a week, though it has cleared considerably.
I did halt the fermentation to early though. The result is a brew that is sweeter then I intended. Next time I would use a yeast nutrient as a lot is going to be missing from the syrup and the tea that the yeast would need. I would also add the splenda after the fermentation was complete. Otherwise, it would be problematic to get the sweetness where you wanted it. I would also make a starter first, and use around 10 grams of yeast in a 1 quart or so starter.
I did not own a hydrometer at that time, so I am unable to determine the ABV.
Based on the additions you made, that may be closer to what you are looking for in a future brew.