Grate the zucchini, sprinkle it with a pinch of salt, let it stand 5 minutes, then squeeze out liquid through cheesecloth or a clean towel. Removing extra moisture keeps the dough light.

In a large bowl whisk olive oil (or butter), sugar, salt, and egg until smooth. Stir in warm milk, then sprinkle yeast over the surface. Wait about 5 minutes until the mixture looks foamy. If no foam appears, start again with fresh yeast and verify milk temperature.

Stir in the grated zucchini. Add 2½ cups flour with cinnamon and nutmeg. Mix until a soft dough forms. If sticky, add flour 1 tablespoon at a time, up to ½ cup more.

Turn the dough onto a floured counter and knead 5 – 7 minutes until smooth and springy (stand-mixer dough hook on medium works too). Place in a greased bowl, cover, and let rise in a warm spot about 1 hour or until doubled. A briefly warmed but switched-off oven makes a dependable proof box.

Beat cream cheese with chopped basil until uniform. Chill for 5 minutes if it feels loose; a slightly firm filling spreads without tearing dough.

Punch down dough and divide in two. Roll each half into a 1/4-inch-thick rectangle. Spread half the filling on each piece. Roll up from the long edge, pinch seams, then slice each log lengthwise to reveal filling. Twist the two strands together and tuck ends under. Lightly flatten the braid so it bakes evenly.

Grease two standard loaf pans. Place a braid in each pan, cover, and let rise 30 – 40 minutes until puffy.

Preheat oven to 350 °F (175 °C). Brush tops with beaten egg, add pumpkin seeds if desired, and bake 35 – 40 minutes. If tops brown early, tent with foil after 25 minutes. Loaves are done when the bottoms sound hollow or an instant-read thermometer reads 190 – 200 °F (88 – 93 °C).

Rest loaves in the pans 10 minutes, then transfer to a rack. Cool completely for clean slices and the best crumb.