In a saucepan, whisk together the cream, milk, vanilla bean seeds, egg yolks, sugar (reserving 2 tbsp sugar for later) and the salt.
Heat the custard over medium heat, whisking constantly, until it begins to steam and just bubble slightly around the edges. Do not let it boil.
Remove the custard from the heat, and pour through a mesh strainer to remove any bits of cooked egg. Cover and refrigerate the custard until thoroughly chilled, preferably overnight.
In a bowl, combine the chopped strawberries with the vodka and the remaining 2 tbsp sugar. Stir and let sit for several minutes until the sugar is dissolved. Scrape the mixture into a small food processor, and pulse a few times to finely chop the fruit. It should resemble the texture of slightly chunky strawberry salsa, but not a smooth puree.
Pour the custard into your ice cream maker and churn according to the manufacturer's instructions. Halfway through the churning, add the strawberry mixture, including all the liquid. Finish churning the ice cream until it has a soft serve consistency.
Transfer the churned ice cream to lidded containers, and freeze until firm enough to scoop, at least 8-10 hours, or overnight.