Heat the oven to 325°. Bring water to a simmer for the water bath. In a medium saucepan, bring the milk almost to a simmer, stirring occasionally.
In a medium bowl, whisk together the eggs, egg yolks, sugar, and salt until just combined. Pour the hot milk over the egg mixture, whisking. Stir in the vanilla. Strain the custard into a large measuring cup or pitcher and skim any foam from the surface.
Divide the custard among four 6-ounce custard cups or ramekins. Sprinkle the tops with the allspice and put them into a small roasting pan. Pour enough of the simmering water into the roasting pan to reach about halfway up the side of the custard cups. Carefully transfer the roasting pan to the middle of the oven and bake until a knife stuck in the center of the custard comes out clean, 45 minutes to 1 hour. Remove the cups from the water bath and let cool. Refrigerate until cold, at least 1 hour.