For the ice cream: Combine the eggs, granulated and brown sugars, the bourbon (if using), vanilla extract, salt and cinnamon in a large glass or ceramic bowl. Stir with a flexible spatula until well combined, then place the bowl over a large pan of gently bubbling water. Stir and scrape continuously until the mixture registers 160 degrees on a digital/instant-read thermometer. This should take no more than 10 minutes, so adjust the heat as needed to keep things moving along. Transfer the bowl to a cool work surface.
Use a handheld electric mixer to beat the warmed egg-sugar mixture until pale and thick enough to hold soft peaks, about 15 minutes (the timing will vary with the power of the mixer). When properly mixed, the mixture will be thick enough to mound up on itself in the bowl when dropped from a spoon.
Whip the cream to stiff peaks in a separate large bowl, then add about one-third of the foamed egg mixture, whisking by hand to incorporate. Add the remaining egg mixture, and fold until well combined.
Scrape into a 2-quart glass or ceramic baking dish, cover with plastic wrap, and place in the freezer. If you plan to use either of the 2 mix-ins (see options, below), let the ice cream freeze for about 1 hour, until thick and firm, before folding it in.
With or without the optional mix-in, continue freezing until the ice cream reaches 0 degrees before scooping. Serve as you would traditional ice cream, in ice cream cones or chilled bowls.