In a mixing bowl, combine the warm milk and sugar. Sprinkle the dry yeast over the top and let it sit for about 5-10 minutes until frothy. If using fresh yeast, dissolve it in the warm milk.
Add the yogurt, vegetable oil, and two eggs to the yeast mixture. Whisk until smooth. Gradually add the flour and salt, mixing until a soft dough forms.
Turn the dough onto a lightly floured surface and knead for about 8-10 minutes until it’s smooth and elastic. You may need to add extra flour while shaping.
Place the dough in a greased bowl, cover it with plastic wrap, and let it rise in a warm place for about 1-2 hours, or until doubled in size.
Once the dough has risen, punch it down to release the air. Turn it out onto a floured surface. Roll it into a rectangle about 1 cm thick.
Evenly spread the basil pesto over the rolled-out dough, leaving a small border around the edges.
Starting from one long edge, roll the dough tightly into a log. Cut the log in half lengthwise, revealing the beautiful layers.
Twist the two halves together and place them into a greased loaf pan. Cover with plastic wrap and let it rise again for about 30-45 minutes.
Preheat your oven to 180°C (350°F) while the dough is rising.
Once the babka has risen, whisk the remaining egg and brush it over the top. Sprinkle with poppy and sesame seeds for that extra crunch.
Bake in the preheated oven for 30-35 minutes, or until the babka is golden brown and sounds hollow when tapped.
Let the babka cool in the pan for about 10 minutes before transferring it to a wire rack. Slice and enjoy warm or at room temperature!
