Pineapple Syrup: Place 4 cups fresh diced pineapple and 1 cup light simple syrup (1 part sugar to 2 parts water) in a resealable freezer bag and evacuate air using a food sealer or the water displacement method. Place in water bath at 135°F for 8 hours. Strain through a fine-mesh strainer or cheesecloth to produce a clear syrup.
Mandarin Syrup: Zest and juice 4 mandarins. Place in a resealable freezer bag with ½ cup light simple syrup (1 part sugar to 2 parts water) and evacuate air using a food sealer or the water displacement method. Place in water bath at 135°F for 8 hours. Strain through a fine-mesh strainer or cheesecloth to produce a clear syrup.
Toasted (Toasted) Coconut Meringue: Toast 1 cup dried shredded unsweetened coconut in a nonstick pan over medium heat, stirring constantly, until golden brown. Place in a resealable freezer bag with 1 cup rich simple syrup (2 parts sugar to 1 part water) and evacuate air using a food sealer or the water displacement method. Place in water bath at 135°F for 8 hours. Strain through a fine-mesh strainer or cheesecloth to produce a clear syrup, and refrigerate until the coconut fat has risen to the surface and solidified, about 2 hours. Skim off the fat and discard it. Note that leaving any significant amount of fat in the mixture will cause the meringue to break. Beat 4 egg whites and ½ tsp cream of tartar using a stand or hand mixer until soft peaks form. Meanwhile, heat ½ cup of the toasted coconut syrup to 240°F over medium heat. Slowly pour in the hot syrup while beating on high, and continue beating until stiff, shiny peaks form.
To Assemble Cocktails: Heat pineapple syrup to boiling, then remove from heat. Add Jello powder and stir until completely dissolved, about 2 minutes. Add other ingredients (mandarin syrup, lime juice, and water or rum) and stir to combine. Pour into plastic shot glasses and refrigerate until set. To garnish Nauvoo cocktails, pipe swirls of meringue directly onto set Jell-O surface, then add a cherry and pineapple slice. To garnish Behemoth cocktails, pipe swirls of meringue onto aluminium foil and toast with a kitchen torch or broiler, then use a butter knife to slide off and gently transfer them to set Jello surface. Makes 6 servings.