Rub inside of a large saucepan with cut sides of garlic. Finely grate garlic into saucepan; add beer and 1 1/2 cups wine and bring to a boil over medium heat. Whisk cornstarch and remaining 1/2 cup wine in a small bowl until no lumps remain, then whisk into liquid in saucepan. Bring to a boil, whisking constantly, then reduce heat so mixture is at a very low simmer and very gradually add Gruyère and Babybel, whisking until smooth (fully incorporate each batch of cheese before adding more).
Whisk bourbon and baking soda in a small bowl to combine, then whisk into fondue, followed by lemon juice; season with salt. Transfer to a fondue pot and serve with bread, ham, salumi, pickles, and crudités for dipping.
