Heat olive oil and 1 tablespoon butter in a large pot over medium-high heat. Add onion, carrots, celery, potatoes, and garlic. Cook 8–10 minutes, stirring occasionally, until softened. Add cauliflower, thyme, oregano, salt, and pepper. Stir to combine.

Add chicken stock and bring to a boil. Reduce to a gentle simmer, cover, and cook 10–15 minutes or until veggies are tender.

In a separate small pot, melt remaining 4 tablespoons butter. Sprinkle flour evenly over butter, whisking constantly for 1 minute. Gradually add milk, whisking continuously, and cook 5–6 minutes until thickened (do not boil). Remove from heat and stir in shredded cheddar until melted.

Reduce soup heat to low. Stir cheese sauce into the soup pot. Taste and adjust seasoning with salt and pepper as needed. For extra creaminess, blend 1–2 cups of soup and stir back in.

Ladle into bowls, garnish with extra cheese and thyme if desired, and serve with buttered bread.