Break peanuts into halves with your hands. Toast in a frying pan over a low heat until they become lightly brown. Coarsely chop them into smaller pieces (or crush them with a rolling pin).
Toast sesame seeds the same way.
In a non-stick pan over a low heat, melt butter then add sugar. Stir from time to time. Cook until it turns into a brown, smooth and sticky consistency (see note 1).
Pour in peanuts and sesame seeds. Stir quickly until well combined. Turn off the heat.
Put the mixture onto a sheet of baking paper placed over a chopping board. Put another sheet over (See note 2). Press the mixture into a flat block with the rolling pin. Cut the block into desired size and shape (See note 3).
When completely cool, store brittle in an airtight container placed in a dry, dark place. Consume with 1 month.
Notes
1. Do not overcook the sugar, otherwise you are likely to get a burnt flavour. It takes me about 10 minutes but the cooking time may vary. 2. As you need to move very fast when the mixture is ready, I suggest you have the baking paper ready before you start cooking the sugar.3. The melted sugar hardens very quickly when the temperature drops. This is why you need to cut the block into pieces as soon as possible.4. Peanuts and sesame seeds are classic choices for Chinese brittle. Please feel free to choose your preferred ingredients. Walnuts, cashew, hazelnuts are great too. Just make sure you toast and chop them before mixing with the sugar.