Measure out 2 tbsp whole milk and 100 ml apple cider. In a saucepan, combine milk, apple cider, cinnamon, nutmeg, coriander, and salt. Simmer over low heat for 2 minutes to infuse the spices.
In a mixing bowl, whisk together the bloomed spices, remaining milk, apple cider, coffee, water, heavy cream, maple syrup, and vanilla extract until well blended.
Turn on the slushie machine. Set it to frappe mode, and start running the machine.
Add the xanthan gum right before pouring in the apple cider frappe base. Whisk to evenly disperse the gum. Add the base to the slushie machine. Let it run until it becomes cool. For a creamier base, let the slushie machine run on 'cool' for 30 minutes.
In a heavy-bottomed saucepan, combine sugar, syrup, and water. Stir gently just to combine, then cook undisturbed over medium-high heat until it reaches 300°F.
Do not stir the caramel as it cooks, this can cause crystallization. If needed, gently swirl the pan to help it cook evenly.
Reduce heat to medium-low. Slowly pour in the warmed cream while whisking. The mixture will bubble vigorously. Once the bubbling subsides, stir in the salt, butter, and vanilla until smooth and glossy.
Check the thickness of the caramel by dipping a spoon into the mixture. If the sauce is too thick and doesn’t run down the back of the spoon, stir in a little water until it reaches your desired consistency. The caramel should ribbon off the spoon slowly. Set aside to cool, then pour into a squeeze bottle.
Combine heavy cream, powdered sugar, and vanilla extract in a bowl. Transfer to a siphon, charge with two N₂O canisters (for a 1 L siphon). Refrigerate until ready to use.
Pour out granulated sugar on a plate. Cut a piece of citrus into quarter wedges. Run the cut side of the citrus around the rim of a wine glass. Press the glass and turn a little bit at a time to frost the rim segment by segment. Set aside to let the sugar dry and harden, about 5 minutes.
Choose a point about ½ inch below the rim inside the glass, then squeeze and turn the glass to create a caramel ring. The caramel will then run down the inside of the glass.
If the caramel has cooled too much by this point, microwave in 10-second bursts to warm it up.
Dispense the apple cider frappe into the wine glass, stopping just before the glass completely fills up.
Top with whipped cream and slide an apple cider donut over the straw for garnish (if available). Serve immediately.