Cook Candied Ham: Heat butter in a large pot or Dutch oven over medium-high heat. Add the diced ham, brown sugar, dijon, honey, cinnamon, nutmeg, cloves, salt and pepper. Cook, stirring constantly, until the sugar is dissolved and the ham pieces are sticky and coated with a glaze (candied), around 10-15 minutes. Remove the candied ham from the pot and set aside. Leave any remaining glaze in the pot.

Sauté the Aromatics into Butter-Flour Roux: In the same pot with the residual ham glaze, add the onions, carrots, celery, garlic. Cook covered over medium-high heat, stirring occasionally, until the onions are softened and translucent, around 8-10 minutes. Add flour and cook, stirring constantly, until the mixture is pasty and a light blonde roux, around 1 more minute.

Build the Broth: Add the Yukon gold potatoes, chicken broth, thyme, and bay leaves to the pot. Bring the mixture to a boil over high heat, then immediately reduce the heat to low and simmer. Cook, stirring occasionally to prevent sticking, until the potatoes are fork-tender, around 20-30 minutes.

Final Touch of Gouda Goodness: Remove the bay leaves and remove the pot from the heat. Let cool for 5-10 minutes to prevent curdling in this step. Stir in the heavy cream (or half and half). Return the pot to the stovetop over medium-low heat. Add the Gouda cheese in three or four small batches. Stir constantly until the Gouda is completely melted and smooth before adding the next batch. This will take around 5 minutes for all batches.