Alcohol is used for extracts because the flavor compounds (plant oils) you are trying to extract do not easily dissolve in water. Alcohol (typically bourbon or vodka) will do the trick. Make sure you use +80 proof because it also acts as a preservative.
Making Mint Extract
To make an extract, tear up or coarsely chop and bruise washed mint leaves into a measuring cup (you'll end up with about twice the volume of extract as you have leaves). Transfer the leaves to a glass container with a tight-fitting lid. Add about twice the alcohol (by volume) as you had leaves. Cover and shake.
The mint leave will tend to float to the top, but give it a chance. After a few days, they'll start to bog down with alcohol and sink. Shake it every few days or so. After a month, you'll have mint extract. Strain the leaves and store.
Adjusting the Strength of Your Extract
The longer you let the leaves steep, the stronger the extract will become until all the oils are essentially spent. You can sample the extract along the way until you get something to your liking. If you want something stronger, you can add fresh leaves to your strained extract and continue the process. There's a limit though; as the alcohol become saturated, you'll get diminishing returns by adding more leaves.
Freezing the extract will not congeal the oils for further separation. They're essentially dissolved in the alcohol (unlike water + oil) and the alcohol will not freeze. Extracts are typically too concentrated to drink straight. For all that effort, it's better just to crush a few leaves directly into a drink with whatever ingredients will make it a proper cocktail.
Boiled Leaves isn't Really Mint Extract
The boiling water method you mentioned above wont achieve the same results. Even if concentrated, the flavor compounds in extracts are typically somewhat volatile (which is why you add them near the end of cooking). You're basically making concentrated, flavored mint water… but it isn't really an extract. And without the alcohol acting as a preservative, you're mint water will have a somewhat limited shelf life. Even distilling the volatile oils by boiling and condensing into a liquid might get you pure mint oil, but that would likely need very specialized equipment.