Easy to make in your ice cream maker and beats store-bought any day. A rich custard base with both vanilla extract and vanilla paste for deep, complex flavor.
Beat eggs and egg yolks in a medium sized bowl. Add sugar and whisk together.
Add heavy cream and half and half to a large saucepan and heat gently — do not let it come to a boil.
Temper the eggs by slowly pouring 1 cup of the hot cream mixture into the egg mixture while whisking quickly. This raises the temperature of the eggs carefully without scrambling them. Then, while stirring, pour the tempered egg mixture slowly into the remaining cream mixture in the saucepan.
Gently heat the ice cream base over medium-low heat, stirring constantly (especially the corners of the pot), until thickened and it reaches 170°F (77°C) on a digital thermometer. The mixture should look silky and coat the back of a spoon so that when you run your finger through it, it doesn't come back together.
Remove from heat and add a small pinch of flour and the vanilla extract and vanilla paste.
Strain through a fine-mesh sieve (to catch any cooked egg pieces) and chill in an ice bath (a bowl set inside a bowl of ice water) until cooled to room temperature. Cover with plastic wrap and refrigerate until completely cold, about 2–3 hours.
Once completely cooled, add the mixture to an ice cream maker according to the manufacturer's instructions and freeze.