In a large mixing bowl, beat the butter and both sugars until creamy. Add the vanilla and almond extracts and beat well. Add the eggs one at a time, beating until mixed.
Mix or sift together the flour, baking soda and salt. Stir flour mixture into the butter mixture, mixing until blended.
Mix in the chips and peanuts. Drip by rounded teaspoonfuls onto a baking sheet sprayed with nonstick cooking spray. Bake in a 375 oven for 10 to 12 minutes.
Let cool on the baking sheet for 5 to 10 minutes, then remove to a cooling rack.