Combine the water, sugar, cream of tartar and corn syrup in a medium-size heavy saucepan fitted with a candy thermometer. Bring to a boil over medium heat. After it boils, stir the mixture occasionally. Boil the mixture until it reaches 340 degrees F. The color should be deep golden brown. Remove from the heat and, working quickly, stir in the cinnamon with a wooden spoon. Stir in the butter until melted, then the peanuts and baking soda.
Pour the mixture onto the oiled cookie sheet with sides and spread it out a bit with the back of a wooden spoon, to about 1/4-inch thickness (it may not fill the whole pan). Let harden, uncovered, in a cool place, 30 to 45 minutes. (To wash the saucepan, soak it overnight.)
Using your hands, and wearing cotton or plastic gloves if desired to keep off any fingerprints, break the brittle into pieces. Store in an airtight container.