In a small pan over medium heat saute the onion with 1 tablespoon of butter until translucent and fragrant.
Add the onion to your slow cooker.
To the slow cooker add your carrots, broccoli and broth.
Stir in seasonings, mustard and hot sauce.
Cover and cook on low for 4 hours.
Turn the slow cooker to high.
In a pot on the stove over medium heat melt your ¼ cup butter and whisk in the ¼ of flour.
Whisk until smooth and thick.
Whisk your evaporated milk into the flour butter mixture.
Whisk until smooth and starts to thicken.
Whisk the milk mixture into the slow cooker.
Add the cheese to slow cooker and cover.
Cook another 1 hour.
Serve!