Combine 1 tablespoon Key lime zest in a bowl of a food processor with ¾ cup of granulated sugar. Process until the zest is very fine.
Place the zest and sugar in a heavy bottom saucepan. Add 2 cups of whole milk and cook on medium heat until the mixture reaches 170°F on an instant-read thermometer. Remove from the heat, cover with a lid and steep for 30 minutes.
While the milk is steeping, whisk the egg yolks with the remaining ¼ cup of sugar in a non-reactive medium bowl. Whisk until the eggs are foamy and slightly thickened. Set aside. Juice the limes and measure to ⅓ cup.
In a separate clean, large glass or stainless steel bowl, add the heavy cream. Set the bowl over an ice bath and place a fine-mesh sieve over the cream.
Put the steeping milk and zest mixture back on medium heat until it reaches 170°F stirring occasionally to prevent scorching.
Temper the eggs by pouring in a slow, steady stream of hot milk while whisking continuously. Once most of the hot milk has been added to the egg yolks, pour the new egg and milk mixture (custard) back in the saucepan. Heat on medium stirring continuously with a wooden spoon or heat proof spatula until it reaches 185 degrees or is thick enough to coat the back of the wooden spoon. Take care not to let the mixture boil. If needed, blend or emulsify the custard if it is not smooth.
Pour the heated custard through the sieve into the cold cream. Stir occasionally until the mixture is fully cooled, about 30 minutes. Add the lime juice and vanilla and stir until combined. Remove the bowl from the ice bath and dry the bottom with a kitchen towel. Cover the bowl and refrigerate for at least 8 hours or overnight.
Process the gelato in your ice cream maker according to the manufacturer directions. Scoop a layer of gelato into an airtight container. Top with a layer of crushed graham crackers, and then another layer of gelato. Repeat topping the final layer of gelato with the last of the crackers. Cover and freeze until set and ready to serve. Sprinkle each bowl with additional crushed graham crackers if desired.