Begin by finely chopping the fennel bulb, celery, and yellow onion. A food processor works wonders for this task, saving you time and ensuring even pieces. Aim for a consistency that will blend beautifully into the stew.

In a large saucepan, melt butter over medium-high heat until it bubbles. Next, add your chopped vegetables. Sauté them for about 5-7 minutes, stirring frequently, until they soften and turn translucent.

Once your vegetables are softened, sprinkle in self-rising flour, stirring continuously until it is fully absorbed. Allow the mixture to cook for 8-10 minutes, stirring occasionally, until it becomes bubbly and turns a light golden color.

Gradually pour in crab base, followed by heavy cream, cooking sherry, half-and-half, and whole milk. Stir everything together thoroughly and bring it to a gentle boil over medium heat.

Once boiling, reduce the heat to low, allowing your stew to simmer gently for 8-10 minutes. Stir occasionally to prevent sticking and ensure even thickness.

Remove the saucepan from heat and gently fold in fresh crab meat, taking care not to shred it too much. Season the stew with salt and pepper to enhance the flavors, adjusting to your taste.