Position a rack in the middle of the oven. Preheat the oven to 350°F. Line 2 or 3 baking sheets with parchment paper.
Sift the flour, baking soda, and salt into a medium bowl and set aside.
In a large bowl, using an electric mixer on medium speed, beat the butter, brown sugar, and granulated sugar until smoothly blended, about 1 minute, Stop the mixer and scrape the sides of the bowl as needed during mixing, Add the egg and vanilla and mix until blended, about 1 minute. The mixture may look slightly curdled. On low speed, add the flour mixture, mixing just until it is incorporated, Mix in the chocolate chips, pecans, walnuts, and almonds until evenly distributed.
Use a tablespoon to drop well-rounded tablespoonfuls of dough (about 2 tablespoons each) onto the prepared baking sheets, spacing the cookies 2 inches apart.
Bake the cookies one sheet at a time until the edges are lightly browned and the centers are just slightly colored, about 14 minutes. Cool the cookies on the baking sheets for 10 minutes, then use a wide metal spatula to transfer the cookies to a wire rack to cool completely.
The cookies can be stored in a tightly covered container at room temperature for up to 4 days.
You can add 1 cup of raisins, dried cranberries, or chopped dried apricots to the dough with the chips and nuts. White, bittersweet, or milk chocolate chips, or a combination, can be substituted for the semisweet chips.