Place whole egg and 2 egg yolks into a mixing bowl. Add sugar, corn starch, and salt. Whisk together completely until mixture turns from yellow to a very page creamy color and is slightly thickened, 5 to 8 minutes.
Place milk in a saucepan. Split vanilla bean lengthwise. Scrape the cut side with a paring knife to extract the seeds (paste). Add the seeds to the milk. Heat over medium-high heat, stirring occasionally, until milk just barely starts to simmer and a few small bubbles appear on the surface. Remove from heat. Whisk hot milk into egg mixture, starting with a small splash then incorporating the rest. Pour mixture back into saucepan.
Place pan over medium-low heat and continue to whisk until mixture begin to thicken, 3 to 5 minutes. Remove from heat and let it cool 5 minutes. Add chunks of butter and whisk until butter melts into the warm milk mixture. Pass mixture through a fine mesh strainer to remove and chunks of cooked egg or vanilla seeds. Cover surface with plastic to keep it from discoloring; refrigerate until thoroughly chilled 2 to 3 hours.