Grate the zucchini and squeeze out excess moisture using a fine mesh strainer or cheesecloth. Set aside.
In a large mixing bowl, combine the olive oil or butter, granulated sugar, salt, and egg. Mix until smooth.
Add warm milk and sprinkle the yeast over the mixture. Let it sit for about 5 minutes until it becomes frothy.
Stir in the grated zucchini.
Gradually add 2 1/2 cups of flour along with the cinnamon and nutmeg. Mix until a soft dough forms, adding more flour as necessary.
On a floured surface, knead the dough for about 5-7 minutes until it becomes smooth and elastic. Place the dough in a greased bowl, cover with a cloth, and let it rise in a warm place for about 1 hour, or until doubled in size.
In a medium bowl, mix the softened cream cheese and chopped basil until well combined.
Once the dough has risen, punch it down and divide it into two equal pieces. Roll each piece into a rectangle about 1/4 inch thick.
Spread half of the cream cheese and basil filling evenly over each rectangle.
Roll each rectangle tightly from the long side to form a log. Pinch the ends to seal.
Cut each log lengthwise down the middle to expose the filling. Twist the two strands around each other to form a braid. Pinch the ends together to seal and tuck them underneath.
Grease a standard loaf pan. Place the braided loaf into the prepared loaf pan. Cover it with a cloth and let it rise for another 30-40 minutes.
Preheat your oven to 350°F (175°C).
Brush the tops of the loaves with the beaten egg and sprinkle with pumpkin seeds if desired.
Bake in the loaf pan for about 35-40 minutes or until golden brown and hollow-sounding when tapped on the bottom.
Allow the bread to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely before slicing.
