Line an 8” x 8” (20cmx20cm) pan with parchment paper so it covers the bottom and the sides of the pan.
Add the sugar, water, and lemon juice into a heavy-bottomed saucepan. Mix until it resembles wet sand, then place the pan on the stovetop. Allow the sugar to melt and caramelize over medium heat until it reaches a deep amber color. Do not stir the mixture. If sugar crystals form on the sides of the pan, gently brush them down with a wet pastry brush to help the sugar melt evenly.
Meanwhile, combine the condensed milk, heavy cream, and peanut butter in a bowl. Whisk well and heat until very warm (use a microwave or saucepan).
Once the sugar syrup reaches a deep amber color, carefully pour in the warm peanut butter mixture. Whisk vigorously until fully incorporated.
Add the butter and vanilla extract and whisk until fully incorporated.
Continue cooking the mixture until it reaches 240F (115C). To test doneness without a thermometer, drop a teaspoon of the hot mixture into a bowl of ice-cold water. Wait 10 seconds, then retrieve it. If you can roll the hardened candy between your fingers into a small ball without it melting, the mixture is ready.
Pour the mixture into a prepared pan, smoothing the surface. Sprinkle the chopped peanuts evenly over the top.
Refrigerate the candy for at least 6 hours, or overnight. Once set, cut it into pieces and serve.