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Using an electric mixer, beat the butter and sugars in a large bowl until fluffy. Scrape down sides of mixing bowl. Beat in the eggs and almond extract. Add the flour mixture in 3 parts and stir just until blended. Stir in the chocolate chips and chopped almonds.
For each cookie, drop 1 rounded tablespoonful of dough onto the prepared baking sheets, spacing 1-inch apart (do not flatten dough). Bake until the cookies are golden (cookies will flatten slightly), about 13 minutes. Cool the cookies on the baking sheets for 5 minutes. Transfer to a cooling rack and cool completely. The cookies can be prepared 1 day ahead. Store airtight at room temperature.
Arrange 12 cookies, flat side up, on a baking sheet. Top each with a scoop of ice cream, then another cookie, flat side down, pressing slightly to adhere. Cover and freeze the sandwiches until they are firm, at least 3 hours. Sandwiches can be made up to 4 days ahead. Wrap each sandwich with plastic wrap and keep frozen.