Butter 8x8x2-inch metal baking pan. Combine 2 cups sugar and half and half in heavy large saucepan. Stir occasionally over low heat until sugar dissolves. Set aside. Bring remaining 1 cup sugar and 1/4 cup water to boil in heavy medium saucepan over medium-low heat, stirring until sugar dissolves. Increase heat; continue boiling without stirring until syrup turns deep amber, brushing sides of pan with wet brush and swirling pan, about 8 minutes. Immediately pour caramel syrup into half and half mixture in large saucepan (mixture will bubble). Stir constantly over medium-low heat until caramel dissolves. Attach candy thermometer to side of pan. Increase heat to medium. Continue cooking and stirring until mixture registers 244°F, about 12 minutes. Remove from heat and immediately stir in baking soda (mixture will foam slightly). Add butter and stir to melt. Let stand without stirring until mixture cools to 160°F, about 20 minutes. Mix in vanilla. Using large wooden spoon, stir constantly until candy begins to thicken and loses its gloss, 4 to 5 minutes. Mix in nuts (candy will be very stiff). Scrape candy into prepared pan. Using wet fingertips, press candy firmly into pan. Cool completely, then cut into 30 squares.