In a large dutch oven, drizzle the olive oil and heat over medium low heat.
Add in the onion and sauté until softened.
Stir in the garlic and cook for additional 30 seconds.
Stir in the flour until a paste forms and cook for 1 minute.
Pour in the broth and evaporated milk, stir until well combined.
Add the broccoli, shredded carrots, and seasonings. Stir to combine.
Measure the cornstarch into a small bowl, then add 1/4 cup of the warmed broth of the soup. Stir this together until smooth.
Whisk the cornstarch slurry into the soup pot.
Cover the pot and turn up the heat to medium. Allow this to cook for 15 minutes, removing the lid to stir occasionally.
Remove the lid and test that the broccoli has cooked and is soft and tender.
Remove from heat, stir in the dijon.
Stir while adding in the cheese until melted. Serve the soup warm.