Start by heating your oven to 400°F so it's fully ready when your tarts go in. Line two baking sheets with parchment paper and set them aside. Having everything prepped ahead means you won't be scrambling once the filling is done.
Warm the olive oil in a skillet over medium-high heat, then add the diced chicken, onion, bell pepper, salt, and spinach. Let it all cook for about five minutes, stirring now and then so nothing sticks or burns. You want the chicken cooked through but still juicy.
Stir in the fresh garlic and cook for just one more minute. The chicken should hit 165°F internally at this point, so I always check with a quick-read thermometer to be safe. Garlic burns fast, so don't walk away here.
Transfer the cooked mixture into a bowl and stir in the pine nuts. Let it cool slightly before adding the Greek yogurt, then mix everything well. Adding yogurt while the filling is too hot can cause it to separate, so give it a minute.
Lay your thawed puff pastry sheets on a cutting board and slice each one into nine even squares, roughly three inches each. Arrange the squares on your prepared baking sheets, leaving a little space between them.
Whisk the egg and water together in a small bowl. Brush this mixture around the edges of each pastry square. This is what gives the tarts that beautiful golden shine once baked.
Spoon about a tablespoon of the chicken filling into the center of each square. Bake for around 15 minutes, rotating the tray halfway through, until the pastry has puffed up and turned a deep golden brown.