Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels. Crumble.
Melt butter in large saucepan over low heat. Stir in onions, celery, and parsnips. Cover and cook, stirring occasionally, until vegetables are very tender, about 10 minutes. Add garlic; cook and stir until fragrant, 1 minute. Sprinkle flour over the mixture and stir constantly until flour dissolves, 3 or 4 minutes.
Slowly stir chicken stock and ale into onion mixture. Add bay leaves and cayenne pepper. Increase heat to medium or medium-high to slowly bring mixture to a boil. Reduce heat to medium-low when mixture starts to bubble; simmer uncovered until soup reaches a smooth consistency, about 1 hour.
Stir heavy cream into soup; add Cheddar cheese. Continue cooking over medium-low heat, stirring occasionally, until cheese has melted and soup is heated through, 3 or 4 minutes. Do not bring to a boil. Sprinkle bacon crumbles on soup.