In a large pot or Dutch oven, melt the butter over medium heat. Add the chopped yellow onion and sauté for about 3-4 minutes, or until the onion becomes translucent and begins to soften.
Stir in the chopped celery and minced garlic. Continue to cook for an additional 5-6 minutes, allowing the celery to soften and the flavors to meld together.
Sprinkle the all-purpose flour over the vegetables, stirring well to combine. Cook for 2-3 minutes, stirring constantly, to create a roux. This will help thicken the soup.
Gradually pour in the chicken broth while continuously stirring to prevent lumps from forming. Bring the mixture to a gentle simmer, allowing it to thicken for about 5-7 minutes. Pour in the whole milk, stirring to combine. Allow the mixture to come to a gentle simmer again and cook for an additional 5 minutes. The soup should thicken further.
Use an immersion blender or carefully transfer the mixture to a countertop blender to puree the soup until smooth. Be cautious when blending hot liquids.
Return the pureed soup to the pot if you used a blender. Season the soup with salt, sugar, and black pepper. Taste and adjust the seasoning as needed. Continue to simmer the soup over low heat for another 10-15 minutes, allowing the flavors to develop and the soup to thicken to your desired consistency.
Once the soup reaches the desired thickness, remove it from the heat and let it cool slightly. To use the condensed cream of celery soup, simply open a jar and dilute with an equal amount of water, milk, or broth, depending on your recipe's requirements. Enjoy the homemade savory flavor in your favorite recipes!