In a small pot, bring 1 cup of heavy cream and ½ cup smooth peanut butter to a simmer over medium heat, whisking often until completely smooth. Remove from heat and chill mixture for 30 minutes.
Once cool, stir in yogurt and vanilla extract. Mix well.
Pour yogurt mixture into the bowl of an ice cream maker and churn according to manufacturer's directions.
Meanwhile, in a small microwave safe container, heat dulce de leche (15 seconds at a time) until it reaches drizzling consistency. If it is too thick, add about a tablespoon of heavy cream to thin out.
When yogurt is frozen, scoop about half into a freezer safe container. Drizzle dulce de leche over top and swirl into yogurt using a butter knife or offset spatula. Top with remaining yogurt and smooth out the top.
Freeze for 2-4 hours to achieve a more solid scooping consistency.