Put candy thermometer on the side of the saucepan, making sure it doesn't touch the bottom.
Put the saucepan over medium heat and cook, stirring, until temperature reaches 240 degrees F on the thermometer. Don't be tempted to turn the heat up to make it go faster!
Add the peanuts and stir constantly until temperature reaches 280 degrees F.
Add butter and continue to stir constantly until temperature reaches 300 degrees F, which is the hard crack candy stage.
Once the temperature reaches 300 F take the saucepan off the heat. Add the vanilla extract and baking soda, stirring constantly. The candy will foam up as the baking soda is added.
The candy syrup is HOT. Be careful during the next step and use oven mitts in case it splashes as you pour. Pour the syrup onto the prepared baking sheet and spread as evenly as possible. Use a spatula or spread it by tilting the cookie sheet. The candy will cool fast, so work quickly.
Let the peanut brittle cool completely, which will take about 30 minutes.
Break into pieces, either large or small, depending on how your are packaging the peanut brittle.
Notes
Store the peanut brittle in an air tight container at room temperature. It will keep for 6-8 weeks. Don't refrigerate it.