Pour 3/4 cup half and half into a small saucepan and heat over medium until hot and steaming with small bubbles at the edges (do not boil). Remove from heat.
In a heatproof bowl, whisk together 2 egg yolks and 1/4 cup sugar until the mixture is pale and slightly thickened.
Temper the yolks: very slowly pour about 1/4 cup of the hot half and half into the yolk mixture while whisking constantly to combine.
Continue to add the remaining half and half in a slow, steady stream while whisking until fully combined.
Return the mixture to the saucepan and cook over low to medium-low heat, stirring constantly and scraping the bottom, until it thickens enough to coat the back of a spoon and registers about 170–175°F (77–80°C). Do not boil.
Immediately pour the custard through a fine-mesh strainer into a clean bowl to remove any cooked bits.
Stir in 2 teaspoons vanilla extract until evenly combined.
Cover the surface of the custard (or cover the bowl) and refrigerate until chilled before serving.