• Preheat the oven to 375°F(190°C). Line 12 non-stick standard paper liners into a regular size 12 cup-cupcake/muffin pan and set aside.

Cream Cheese Filling

• Place the cream cheese, sugar and vanilla extract in a medium bowl and using a spoon press the mixture until completely combined. Set aside the bowl.

Muffin Batter

• Roughly chop half of the walnuts into small pieces with a sharp knife, and the other half into small and very small pieces to use on top of the muffins to give the crumble effect.
• Peel and grate the carrots.
• Place the flour, cinnamon, ginger, nutmeg, baking powder (and salt if using) into a medium bowl and mix.  Set aside.
• Mix the sugar and eggs in a medium bowl with a whisk until just combined for almost 30 seconds or so.
• Mix in the olive oil and vanilla extract, stir with a whisk until just combined.
• Stir in the flour mixture in 2 batches. You can use a whisk in the first batch but then continue with a spatula to mix easily. There can be some visible flour left, that's fine. They'll go in the next step.
• Add the grated carrots and stir with a spatula.  Mix in the walnuts.

Assemble

• Set aside 6 tablespoons of the muffin batter.
• Divide the batter among 12 muffin cases. It is just a little more than 2 tablespoons of batter per case.
• Make a hole in the middle of the batter by using a spoon. As the batter is not too thick, don't expect to make an evident hole. Instead of trying to create holes for each 12 muffin cases, first create a hole and then add a heaping 2 teaspoons of cream cheese filling into the middle.  With the spoon, lightly press to the filling. Then repeat this step for the other muffin cases.
• Use the muffin batter you set aside: Add ½ tablespoon of batter on top of each cream cheese mixture and spread it with a spoon.
• Sprinkle the walnuts on top.
• Bake for 22 minutes or until the top is golden brown and the toothpick inserted from the sides comes out clean. As there is a cream cheese filling in the middle and that part can be wet, try to make the test from the sides to the middle bottom.
• Let the muffins stay in the pan for 10 minutes.  After 10 minutes, gently remove the muffins from the pan and let them cool for at least 25 minutes on a wire rack.