In a medium saucepan, combine all ingredients except the Greek yogurt, vanilla, and egg yolks.
Bring the mixture to a low simmer over medium-low heat until slightly bubbling.
Temper the egg yolks by whisking about 1 cup of the warm pumpkin mixture into the yolks.
Whisk the tempered egg mixture back into the saucepan and continue to simmer for about 5 minutes.
Remove the saucepan from the heat and allow the base to cool to room temperature.
In a small bowl, whisk together the Greek yogurt and vanilla bean paste until smooth.
Whisk the yogurt mixture into the cooled pumpkin base until completely blended.
Cover the mixture and chill in the refrigerator for at least 4 hours or overnight.
Pour the chilled base into an ice cream maker and churn according to manufacturer instructions for about 40 minutes.
Serve immediately for soft-serve consistency, or transfer to a freezer-safe container to freeze firm. If frozen firm, thaw for 30 minutes at room temperature before serving.