Adjust an oven rack to the center position, and preheat the oven to 325 degrees.
Butter an 8-inch square baking pan and set aside.
Sift the flour with the cinnamon, soda, and salt 3 times; set aside.
Measure the peanuts and then chop with a large chef’s knife until medium fine; set aside.
Melt the butter in a heavy 2- to 3-quart saucepan over medium-low heat.
Add the brown sugar and stir constantly with a wooden spoon for 1 minute, until the sugar smells toasty. The sugar and butter will be thick and pasty looking.
Add the heavy cream and raise the heat to medium.
Stir occasionally as the mixture comes to the boil. As soon as the boil is reached (the surface is covered with thick bubbles), boil for exactly 1 minute, stirring once or twice.
Remove the pan from the heat and cool the butterscotch until it feels warm, about 10 minutes.
Beat in the egg with the wooden spoon until smooth, then beat in the vanilla.
Stir in the dry ingredients only until incorporated, then stir in the peanuts.
Spread the batter evenly in the pan.
Bake about 25 to 30 minutes, until a toothpick comes out with a few wet crumbs sticking to it. Do not overbake. These cookies should be very moist.
Set the pan on a wire rack to cool. The sides of the baked “cake” will be higher than the center.
In about 5 minutes, tamp down the sides of the “cake” with your fingertips to level it with the center.
Cool completely and cut into squares.
Store airtight. These keep well for a few days at room temperature.