Line a baking sheet with parchment or waxed paper.
Combine the butter, granulated sugar, brown sugar and heavy cream in a medium heavy saucepan and cook over low heat, stirring occasionally, until the sugar dissolves. Continue to cook until the mixture reaches 300 degrees F, or the hard-crack stage (a drop of boiling syrup immersed in cold water crackles).
Remove from the heat, add the vanilla, and stir. Pour onto the prepared sheet and let cool completely.
Crack the toffee into large shards with a rolling pin. Place the pieces in a large deep pot and break into smaller pieces with the end of the rolling pin. Store in an airtight container until ready to use.
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