In a medium pot, bring milk, cream and 2 Tbsp sugar to a boil.
Meanwhile, in a large bowl, whisk together remaining 1/3 cup sugar and yolks. Once milk mixture has come to a boil, lower heat. Temper hot milk into sugar-yolk mixture. Slowly add hot milk into yolks about 1/4 cup at a time, whisking to distribute heat. Once all the milk has been added to yolk, transfer all contents back to the pot.
Stir over medium-low heat until mixture reaches nappe consistency, or 180 degrees F on a kitchen thermometer. Stir frequently to ensure mixture does not burn at the bottom. Let mixture sit at 180 degrees F for 3 minutes to pasteurize eggs. Remove from heat and add vanilla paste. Stir to combine.
Transfer mixture to an airtight container and let mature in the fridge overnight. Freeze mixture in ice cream maker according to your unit's instructions. Once the volume has increased by half and has reached a soft serve consistency, add in chopped chocolate and caramelized figs. Let run for another 3 minutes to distribute fillings. Transfer ice cream to an airtight container and let rest in the freezer for at least 30 minutes before serving.
Caramelized Figs:
Melt butter in a medium skillet over medium-high heat. Add sugar and stir to combine. Add halved figs to skillet. Toss in sugar-butter mixture. Cook over medium heat, stirring often, until figs have softened and mixture is jam-like in texture. Remove from heat and allow to cool. Roughly chop figs into a smaller chunks. Store in the fridge until ready to use.