Preheat the oven to 180°C (350°F).
Using a food processor, crush the digestive biscuits until they form fine crumbs. Combine the melted butter with the crumbs and mix thoroughly until the mixture resembles wet sand.
Press the biscuit mixture evenly into the base of a 9-inch (23 cm) springform pan to create the crust. Place the pan in the refrigerator while you prepare the filling.
In a large mixing bowl, beat the cream cheese, peanut butter, and granulated sugar until you achieve a smooth and creamy consistency.
Gradually add the eggs, one at a time, and beat well after each addition. Remember to scrape down the sides of the bowl as needed.
Incorporate the sour cream and vanilla extract into the mixture until well combined.
Pour the filling over the prepared crust in the springform pan, using a spatula to smooth the top.
Bake in the preheated oven for 60 minutes or until the edges are set and the centre is slightly jiggly.
Turn off the oven and allow the cheesecake to remain inside for an additional 30 minutes with the oven door slightly ajar.
Take the cheesecake out of the oven and let it cool completely at room temperature.
During the cooling process, prepare the peanut butter sauce. Melt the peanut butter in a small saucepan over low heat, and then stir in the powdered sugar and milk until the mixture is smooth and well combined. Remove from heat and let it cool slightly.
Once the cheesecake has cooled, gently remove it from the springform pan. Drizzle the peanut butter sauce over the top of the cheesecake.
Place the cheesecake in the refrigerator and allow it to chill for at least 2 hours or overnight before serving.