Modern Mexican Chocolate Flan

In a small heavy-bottomed saucepan, combine 3/4 cup sugar with 1/3 cup water and stir to combine. Bring to a boil over moderate heat, using a pastry brush dipped in cold water to wash down any sugar crystals clinging to the side of the pot, then lower the heat and simmer, without stirring, until the syrup begins to color. Swirl the pan continually until the syrup is an even, deep amber color. Immediately divide the caramel among the ramekins, swirling so it coats the bottom of each.
Arrange a rack in the middle of the oven and preheat to 325°F.
In the bowl of a food processor, process the chocolate until it resembles small pebbles. Transfer to a medium saucepan and add the half-and-half, milk, cinnamon stick, and the remaining 1/2 cup sugar. Place over moderate heat and bring to a simmer, stirring occasionally, then remove from the heat, cover, and let steep for 20 minutes.
In a large bowl, combine the eggs, coffee liqueur, and the vanilla and almond extracts and whisk to combine. Slowly pour about 1 1/2 cups of the hot milk/half-and-half mixture into the egg mixture, whisking constantly. Add in the rest of the hot milk and whisk to combine. Pour through a fine-mesh sieve set over a large bowl and divide evenly among the 8 ramekins. Discard solids.
Transfer ramekins to a large roasting pan and add enough hot water to come halfway up the sides of the ramekins. Loosely cover the pan with foil and bake until the custard has barely set (a knife inserted halfway between the edge and the center should come out clean), 35 to 40 minutes. Let cool in the water bath, then refrigerate to chill thoroughly. DO AHEAD: The flans can be made ahead and stored, wrapped in plastic in the refrigerator, up to 3 days.
Just before serving, run a small thin knife around each flan, then invert onto small plates and serve.