For the caramel: Very lightly grease the inside of a 2-cup glass measuring cup with oil. Combine the granulated sugar and butter in a small deep saucepan. Bring to a simmer over medium heat, stirring frequently. (Don't worry if the mixture looks curdled and then separated-it will come together.) Cook, stirring, until it looks like dark peanut butter, 12 to 15 minutes.
Meanwhile, bring the heavy cream to a simmer over medium heat in a small saucepan. When the butter mixture is the right color, remove from the heat and slowly and very carefully whisk in the hot cream-it will bubble up and steam, so be careful. Put the saucepan back over medium heat, bring the mixture back to a simmer and cook about 1 minute. Pour into the prepared measuring cup and cool to room temperature. (The caramel can be made the night before and kept, covered, at room temperature. You can warm it very briefly in a microwave so that it is pourable, but be careful not to overheat. It should not be too loose.)
For the brownie: Preheat the oven to 350 degrees F. Cut a 9-by-20-inch piece of foil. Butter the corners and sides of a 9-by-13-inch baking pan. Line the pan with the foil so that the excess hangs over at each of the short sides of the pan. Put the chocolate and butter in a heatproof bowl and set it over a saucepan of barely simmering water, being careful that the bowl does not touch the water. Stir occasionally with a rubber spatula until smooth.
Whisk the eggs, sugars and vanilla in a large bowl. Stir the chocolate into the egg mixture using a rubber spatula, and then stir in the flour until just combined. Stir in 1 1/2 cups of the peanuts.
Pour the batter into the prepared pan. Drizzle the caramel over the top, using a butter knife to swirl it into the batter. Coarsely chop the remaining 1/2 cup peanuts and scatter over the top. Bake until a toothpick inserted in the center comes out clean, 25 to 30 minutes. Be sure to insert the toothpick in a spot that does not have too much caramel.
Place the pan on a cooling rack and, while it is still slightly warm, run a butter knife between the brownie and the long sides of the pan. Cool completely, about 1 hour.
When the brownie has cooled completely, place a lightweight cutting board or a baking rack over the top of the pan. Flip and set on the counter. Gently pull the pan from the foil and the foil from the pan to remove. Gently peel the foil off the brownie. Place another lightweight cutting board on top, and flip the brownie right-side-up. Slice into 1 1/2-inch squares.