Heat butter and bacon grease in a large pot over medium heat; cook and stir carrots and onion in the melted butter-bacon grease mixture until onion is translucent, 5 to 10 minutes. Season with salt and pepper.
Add 1/2 the thyme to carrot-onion mixture; cook and stir until thyme is fragrant, 10 to 15 seconds.
Stir chicken stock, sweet potato, ginger paste, remaining thyme, salt, and pepper into carrot-onion mixture. Bring to a boil, reduce heat, and simmer until sweet potato is soft and flavors of soup have blended, 15 to 20 minutes. Mix orange juice, brown sugar, and cinnamon into soup.
Puree soup using a hand blender until smooth; mix in more chicken stock to reach desired consistency. Stir half-and-half into soup.
1 tablespoon butter
1 tablespoon bacon grease
1 1/2 cups roughly chopped carrots
1/2 onion, diced
salt and ground black pepper to taste
3 sprigs fresh thyme, leaves stripped, divided
2 cups chicken stock, or more if needed
1 cup roughly chopped sweet potato