In a large pot set over medium-low heat, add the coconut milk, condensed milk, evaporated milk, orange juice, pumpkin pie spice, vanilla and egg yolks. Vigorously whisk to incorporate the yolks and continue whisking until warm, homogenous and frothy, 5 to 8 minutes. (Don't stop whisking! Get a little arm exercise.)
Remove from the heat and stir in the rum and orange liqueur. Chill the mixture over an ice bath. Alternatively, pour the coquito into three 1-liter bottles or a 1-gallon jug and refrigerate until chilled, 2 hours. Serve in shot glasses topped with orange zest and a dash of pumpkin pie spice. You can also serve the coquito in a lowball glass with ice and the same garnish.