COMBINE THE BROCCOLI, ONION, SHREDDED CARROTS, CHICKEN STOCK, SALT, PEPPER, AND NUTMEG IN THE SLOW COOKER AND COOK ON LOW FOR FOUR HOURS.
TURN THE SLOW COOKER TO HIGH.
IN A SMALL SAUCEPAN MELT THE BUTTER. SLOWLY WHISK IN THE FLOUR. GET A CUP OF LIQUID FROM THE SLOW COOKER. VERY VERY SLOWLY ADD IT TO THE SAUCE PAN WHISKING IT IN AS YOU GO. THEN VERY SLOWLY WHISK IN THE HALF AND HALF.
ADD THE FLOUR/BUTTER/HALF AND HALF MIXTURE TO THE CROCK POT AND STIR IT IN TO COMBINE. SLOWLY ADD IN THE CHEDDAR CHEESE. IT WORKS BEST TO ADD ABOUT A 1/4 CUP AT A TIME, STIR IT IN, COVER THE CROCK POT FOR A FEW MINUTES, AND THEN ADD ANOTHER 1/4 CUP UNTIL YOU HAVE USED ALL THE CHEESE.
AFTER ADDING ALL THE CHEESE, TURN OFF THE CROCK POT (NO NEED TO COOK FOR THE FULL HALF HOUR) AND SERVE!
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