Special equipment: a Bundt pan
1. Whisk the yeast into the warm milk in a large bowl. Add the sugar and let stand until bubbly, about 5 minutes. Whisk in the oil and egg until combined, and then whisk in 2 cups of the flour and the salt. Switch to a spatula and fold in the remaining 1 cup flour, 1/2 cup at a time. Mix until the dough is shaggy.
2. Lightly flour a work surface. Scrape the dough onto the floured surface and knead until smooth and firm, about 5 minutes, adding more flour as necessary. Coat a medium bowl with vegetable oil. Turn the dough in the bowl to coat and allow it to rise until doubled, 40 to 45 minutes.
3. Melt 2 tablespoons of the butter in a small skillet over medium heat. Add the Creole seasoning and garlic and cook until the garlic is tender and fragrant, 2 minutes. Remove from the heat and set aside.
4. Grease a Bundt pan with butter. Lightly flour a work surface. Remove the dough from the bowl and knead 5 or 6 times to form into a ball. Roll the dough into a large rectangle, about 12 by 15 inches. Brush with the garlic butter and sprinkle with the grated cheese, parsley and thyme. Starting on the longer side, roll up and seal the edges together, and then form a circle with the seam on the inside. Place the whole parsley leaves on the bottom of the Bundt pan decoratively. Lift the dough circle into the pan and allow it to rise until puffed, 25 to 30 minutes.
5. Preheat the oven to 350 degrees F. Bake until golden brown, 30 to 35 minutes. Place a serving plate over the pan and turn the bread onto the plate. Melt the remaining 1 tablespoon butter and brush over the bread. Serve warm or at room temperature. If the parsley sticks to the pan, carefully remove each leaf and place on the bread after buttering.