Stuff a scant cup of ice cream into the bottom of each of 2 pint glasses. Over each portion of ice cream, pour 3 tablespoons of syrup. Fill each glass with soda water. Stir slightly with a sundae spoon. Serve immediately with a straw.

In a small bowl, whisk together pumpkin purée and miso. Cover and refrigerate for 2 hours.

Combine egg yolks, 1/2 cup cream, and 1/4 cup brown sugar in a medium-sized bowl. Whisk until smooth and the sugar begins to dissolve, about 2 minutes. Set aside.

Combine remaining cream and brown sugar in a heavy 2-quart saucepan. Over medium heat, cook until bubbles form around the edges of the pan, about 5 minutes.

Remove the cream mixture from the heat. Gradually whisk the hot cream mixture into the egg mixture. Pour the resulting custard mixture back into the pan. Cook over medium heat, stirring constantly with a wooden spoon while keeping the custard at a very low simmer until it is thick enough to coat the back of the spoon. Do not allow the custard to boil. Whisk the pumpkin mixture into the custard. Strain through a fine-mesh sieve into a bowl.

Place the bowl with the custard into a larger bowl partially filled with ice water to cool. Once cooled, cover with plastic wrap, pressing it directly on the surface of the custard to prevent a skin from forming. Refrigerate until chilled.

Transfer the custard to an ice cream maker and freeze according to the manufacturer's instructions. Once frozen, transfer the ice cream to a freezer-safe container. Cover and freeze until firm.

Combine sugars and spices in a small pot with 1 cup of water. Place pot over medium heat. Cook, stirring constantly, until the sugar has dissolved. Continue to simmer until the syrup reduces by half. Remove from the heat and cool to room temperature. Add bourbon and lemon juice and transfer to a clean glass jar. Store in the refrigerator for up to 2 weeks.