Build in a copper mug, ideally, or double old-fashioned glass, as shown, adding all ingredients except ginger beer and bitters. Add ice. Add rhubarb bitters and fill rest of mug with ginger beer. Garnish with grilled pineapple wedge.
For grilled pineapple syrup
Remove rind and leaves from whole pineapple. With core remover, core pineapple, then cut in half lengthwise and grill until you have some nice char on the fruit. Remove from grill and let cool. Cut into 1-inch chunks. Add 2 cups pineapple and 3 cups simple syrup to blender, then blend until smooth. Strain through a fine-mesh strainer or cheesecloth. Syrup will last about 1 week in refrigerator.