Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil.
Place bacon slices on the baking sheet and coat with brown sugar only on one side.
Bake in the preheated oven, flipping once half way through, until browned and caramelized, 10 to 12 minutes. Remove bacon from the oven and place on a wire rack. Cool, break into small pieces, and set aside.
Add peanut butter, sugar, and salt to a large mixing bowl. Blend until smooth using an electric mixer. Add milk, mixing on low speed until sugar is dissolved. Stir in the heavy cream and vanilla just until incorporated.
Pour into an ice cream maker and churn according to manufacturer's instructions, about 20 minutes. Gradually sprinkle chocolate chips and crumbled bacon over the ice cream in the last few minutes of churning. Do not over churn because you may dissolve the bacon.
Transfer the ice cream to an airtight container and freeze, 3 hours to overnight.