Possible Clues:

• Dreyer's, by another name
• Competitor of Blue Bell
• Brand in the ice cream aisle
• Breyer's competitor
• 'Grand' brand of ice cream
• Big name in the frozen aisle
• Dreyer's, in Kansas City
• Brand with 'Scooping since 1928' on its cartons
• Competitor of Ben and Jerry's
• 'Slow Churned' ice cream brand