Combine flour, baking soda and salt in medium-size bowl.
Beat together butter and brown sugar in bowl at medium speed with paddle attachment until well mixed, about 1 minute. Beat in vanilla.
Beat in the eggs, one at a time, beating until smooth after each addition. Scrape down sides of bowl and beater. Beat in the flour mixture; then immediately beat in the chopped slivered almonds.
Scrape the dough onto a lightly floured work surface. Divide the dough in half; shape each half into a cylinder, each about 10 inches long and 2 inches in diameter.
Roll a piece of parchment paper or waxed paper tightly around each cylinder of dough, keeping dough as round as possible. Refrigerate until firm. Or, at this stage, the dough can be double-wrapped in plastic wrap and then frozen for up to 3 weeks.
When you are ready to bake the cookies, set the oven racks in the upper and lower thirds of the oven. Heat oven to 350 degrees F. Line 3 to 4 baking sheets with parchment paper or foil.
Slice the cookies 1/4 inch thick, rotating the roll of dough often as you slice so it doesnt become squashed from the weight of the knife as you cut through.
Arrange the cookies on the prepared baking sheets, spacing them about 1 inch apart.
Bake in 350 degree F oven for about 12 to 15 minutes or until cookies have puffed slightly and are dull and firm to the touch.
Slide the paper or aluminum foil with cookies from the sheets onto wire racks to cool. Makes about 80 cookies.