Heat the oven to 220°C / 425°F and line a 12-cup muffin pan with paper liners. The high starting temperature helps build tall domed tops; watch browning closely near the end if using a dark muffin pan.

Mix the cream cheese, sugar, vanilla, and salt in a small bowl until smooth and fully combined, then chill while preparing the rest. The filling should be thick, smooth, and spoonable, not runny; chilling keeps it centered in the muffins instead of dissolving into the batter.

Combine the flour, brown sugar, granulated sugar, cinnamon, and salt in a medium bowl, then pour in the melted butter and mix with a fork until clumps form. Fold in the chopped walnuts. You want irregular crumbs ranging from small sandy bits to pea-sized clusters; add a tablespoon of flour if the mixture seems wet. Chill until needed for better crumb definition.

Whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves in a large bowl, mixing thoroughly so the leavening and spices distribute evenly.

Whisk the eggs, brown sugar, and granulated sugar in another bowl until smooth and slightly thickened. Whisk in the oil, applesauce or sour cream, and vanilla until fully combined, making sure the sugar is mostly dissolved before this meets the dry ingredients.

Add the wet mixture to the dry ingredients and fold gently with a spatula until partially combined. Add the grated carrots, chopped walnuts, and raisins if using, folding just until no dry flour remains. The batter should be thick and scoopable; overmixing here makes the crumb tougher and can reduce the rise.

Divide about half the batter among the 12 muffin cups, then add 1 heaping tablespoon of chilled cream cheese filling to the center of each. Cover with the remaining batter, filling each cup nearly full, about 85 to 90%, then top generously with the streusel, pressing it lightly so it adheres while staying craggy on top. Keep the cream cheese mostly centered and fully covered with batter, so it stays creamy rather than drying out on the surface.

Bake at 220°C / 425°F for 5 minutes, then, without opening the oven, reduce the temperature to 190°C / 375°F and bake for 15 to 19 minutes more. The muffins are done when the tops are domed and browned, the streusel is set and lightly crisp, and the crumb around the center tests clean with a few moist crumbs; by thermometer, the crumb (avoiding the cream cheese center) should read about 96–98°C / 205–208°F. Tent loosely with foil for the last few minutes if the tops are darkening too fast.

Let the muffins cool in the pan for 10 minutes before transferring to a rack. This short rest lets the crumb set and the cream cheese center thicken slightly. Serve warm or at room temperature.