Preparation Whisk first 5 ingredients in medium bowl to blend. Using electric mixer, beat butter and both sugars in large bowl until light and fluffy. Add eggs and vanilla, beating to combine. Add dry ingredients and beat until just blended. Stir in chocolate chips and walnuts. Cover dough and chill 1 hour. (Can be made 1 day ahead. Keep chilled. Let soften slightly before continuing.) Arrange 2 racks in center of oven; preheat to 350°F. Butter 2 baking sheets. Form dough into balls, using 1/4 cup dough for each. Place on prepared sheets, spacing 2 inches apart. Flatten with hand to 3 1/2-inch rounds. Bake 10 minutes, then rotate sheets. Bake until cookies are golden brown around edges and firm in center, about 4 minutes longer. Cool on sheet 5 minutes. Transfer to racks to cool completely. (Can be made 1 week ahead. Store airtight at room temperature.)