I know cordials are meant to be non-alcoholic but I like mine with alcohol. I suppose I could refer to them as infusions but that sounds like a herbal tea.
In case you haven't got the idea yet, what I do is take some strong alcohol - a bottle of cheap vodka for example - and add berries or herbs to make a flavoured alcohol. It's not brewing but the end result is similar.
A couple of suggestions.
A half-pint mug of elderberries washed and drained added to 1 litre of alcohol for a week or more then strained makes a rich fortified wine-like drink.
Sloes (obviously) take a similar process but it's worth waiting a bit longer, say 6 weeks.
Two sprigs of rosemary (about the size of a ladies hand), a similar bunch of basil leaves, a small pinch of thyme (not too much - it makes the flavour harsh) and a dessert spoon of dark sugar in a litre of alcohol. This produces a drink like vermouth (Martini) with a slightly Christmasy flavour (to quote my daughter). Leave the herbs in the alcohol for a week before straining then add the sugar.
All these can be drunk immediately after the infusion is finished but can stand for a few months as well. I keep the alcoholic content high when storing in order to prevent any decay. The drink can be diluted in the glass after all. All the recipes here are just a starting point from which to develop your own favourites.
The vermouth mix is a useful flavouring for sauces when cooking as an alternative to fresh herbs and the berry based drinks can be added to ice cream or dessert sauces.
I tried strawberries, blackberries, blackcurrants but the results, while very pretty pink, didn't taste of much. Perhaps a longer infusion would have helped.
I should mention that I try to use fruit and herbs that I grow or at pick myself. That makes the process seasonal to some degree. Even the herbs are best picked when growing strongly so they aren't very good in the Winter!
NN