In a large pot (a 4-quart or larger works well), heat the olive oil over medium heat.

Toss in the diced carrots, celery, and onions. Season lightly with salt and pepper. Sauté for about 5 minutes, or until the veggies start to soften.

Stir in the flour and let it cook for another minute, continuing to stir.

In a separate bowl, combine the water and chicken base. Add this mixture to the pot along with the broccoli and cauliflower.

Bring the soup to a boil, then lower the heat to a simmer. Cover with a lid and let it simmer until the veggies are tender, which should take about 10 minutes.

Remove from heat and use a potato masher to mash the veggies to your desired consistency.

Stir in the half-and-half and shredded cheddar cheese. Keep stirring until the cheese is fully melted. Taste and adjust seasoning, if necessary.