Preheat the oven - Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Make the filling - In a small bowl, mix together the cream cheese, sugar, lemon zest, and vanilla extract. Add in the egg yolks and mix until well combined. - Be sure to mix the egg yolks in thoroughly to avoid any lumps in the filling.
Prep the phyllo dough - Lay out the phyllo dough and cover with a damp towel to prevent it from drying out. Melt the butter in a small saucepan or in the microwave. - Be gentle when handling the phyllo dough, as it tears easily. It can be helpful to brush the melted butter over the phyllo sheets as you layer them to help prevent tearing.
Layer the phyllo dough and filling - Carefully lay out one sheet of phyllo dough and brush with melted butter. Repeat with 3-4 more sheets of phyllo dough. Spread half of the cream cheese filling on top of the layered phyllo dough, leaving a few inches of space at the edges. Layer 3-4 more sheets of phyllo dough on top of the filling, brushing each layer with butter. Spread the remaining cream cheese filling on top, leaving a few inches of space at the edges. Layer the remaining phyllo dough sheets on top of the filling, brushing each layer with butter. - It's important to work quickly when layering the phyllo dough, as it dries out fast. A damp towel can help keep the phyllo moist if you need a break. Don't worry if the edges of the dough tear or crinkle - it's part of the charm of homemade pastry!
Bake the strudel - Brush the top of the strudel generously with melted butter, then bake for 40-45 minutes until golden brown and crispy. - Keep an eye on the strudel in the oven - it can brown quickly towards the end of the baking time. If it starts to brown too fast, cover it loosely with foil.
Serve and enjoy - Remove from the oven and let cool slightly. Dust with powdered sugar and slice into portions. Serve warm and enjoy! - This sweet cheese strudel is best served warm, but can be enjoyed at room temperature as well. It pairs perfectly with a cup of coffee or tea for a mid-day treat.