Drain clams, reserving liquid. Chop half of the clams; set chopped and whole clams aside. Add enough water to the reserved clam liquid to measure 1 1/2 cups; set clam liquid aside.
Coat a large saucepan with cooking spray; heat saucepan over medium heat. Add bacon, onion, and celery to saucepan. Cook for 5 to 8 minutes or until onion is tender and bacon is cooked through, stirring occasionally. Remove bacon from pan; drain on paper towels. Chop bacon and set aside.
Stir potatoes, cauliflower, thyme, pepper, and reserved clam liquid into onion mixture. Bring to boiling; reduce heat. Simmer, covered, for 10 to 12 minutes or until potatoes are tender. Remove from heat; cool slightly. Transfer half of the potato mixture (about 2 cups) to a blender or food processor. Cover and blend or process until smooth. Return to the remaining potato mixture in saucepan.
In a medium bowl, whisk together milk, half-and-half, and flour until smooth. Add all at once to potato mixture. Cook and stir just until boiling. Stir in chopped and whole clams and carrots. Return to boiling; reduce heat. Cook for 1 minute more. Sprinkle each serving with chopped bacon.