Combine brown sugar, water, and apples in a medium saucepan. Heat to boiling and simmer for about 20 minutes, stirring occasionally to prevent burning. Skip this step if you're using pre-made apple syrup.
Once the apples are soft and the sugar has completely dissolved, pour into a strainer over a bowl. Take a spoon and smash the apples to remove as much juice as possible. Pour into a jar and allow to cool.
Add espresso, ground cinnamon, and ground ginger to a French press. If using a regular drip brew, simply add the spices to the ground coffee and brew twice as strong as you generally would brew.
Add boiling water to the French press and allow to brew for 4-5 minutes. Once done, depress the plunger and pour the espresso into an alternate container or small pitcher.
Fill a Mason jar with ice and pour espresso to fill the jar 2/3 of the way. Add 1-3 tablespoons apple syrup. Cover and shake for 30 seconds.
Combine the oatmilk and vanilla in a milk frother, creating cold foam. You can alternately use a mixer or handheld frother.
Pour the oatmilk froth into the Mason jar and enjoy!