Preheat your oven to 375°F (190°C).
In a bowl, mix the whole wheat flour with a pinch of salt. Add the egg and olive oil, and gently knead until a smooth dough forms. If needed, add a teaspoon of water. Cover and let rest for 20 minutes.
Meanwhile, in another pan, heat a splash of olive oil over medium heat. Sauté the diced onion, carrot, and bell pepper until they soften, about 5 minutes. Add the chopped spinach and cook for an additional 2 minutes.
Stir in the cooked red lentils, ground cumin, coriander, and smoked paprika. Remove the pan from heat and gently fold in the crumbled feta cheese. Allow the filling to cool slightly.
For the zesty green chutney, combine Greek yogurt, chopped fresh cilantro, lemon juice, green chili (finely chopped), and minced garlic in a small bowl. Mix well and season with a pinch of salt as desired.
Divide the rested dough into two portions on a lightly floured surface. Roll each portion into a thin circle. Spoon the lentil and vegetable filling onto one half of each circle, leaving a border at the edges.
Fold the dough over to cover the filling, pressing the edges to seal. You can crimp the edges with a fork for a decorative touch.
Place the assembled hand pies on a baking sheet lined with parchment paper. Bake in the preheated oven for 20-25 minutes, or until the crust is crispy and golden.
Remove from the oven and let cool slightly before serving with the zesty green chutney on the side.