I usually make these turnovers with homemade rough-puff pastry (also called blitz pastry) because it tastes better, but I won't blame you if you use commercial puff pastry. It's worth seeking out all-butter puff, and it's even better if you buy it in a block, rather than rolled out sheets, which are too thin.
My favourite jam to use as a filling is homemade mango jam - it has a bright, summery taste and the mango flavour is very pure. You can make it with other types of jam, but try the mango version first. Whichever jam you choose, check the consistency - if it's too runny, simmer it in a saucepan until it becomes thick but spoonable, then refrigerate it until cool, before using it in the turnovers.
On a lightly floured work surface, roll out the puff pastry into a large rectangle that’s just a little larger than 30cm x 45cm (12 in x 18 in). Trim the edges of the dough, so it’s even.
Starting at one long side, roll the dough tightly until you reach the other long side. Put the “snake” of dough seam-side down on a baking tray lined with parchment paper and refrigerate for about 30 minutes.
Cut the dough roll into 16 even pieces. Place most of the dough in the fridge and work with only one or two pieces at a time.
Place a piece of dough with one cut side up on the work surface and roll it into a circle 10cm to 11cm (4 in to 4 ⅓ in) in diameter (it’s easiest if you use a small rolling pin). As you finish rolling out the circles, lay them, slightly overlapping, on a parchment-lined baking tray. When you finish rolling out all 16 circles, put the tray in the fridge for about 30 minutes.
Preheat the oven to 250° Celsius (480° Fahrenheit). Whisk the egg.
Very lightly brush egg over the edge of half the circle of dough (if you use too much egg, the edges won’t adhere when you press them together later). Put a spoonful of jam in the centre of the circle then fold it in half and tightly press the edges together.
Crimp the edges to seal in the filling, then place the jam turnover on a parchment-lined baking tray. Finish filling, sealing and crimping all the turnovers and lay them on the tray.
Very lightly brush egg on the turnovers, then use scissors or a very sharp knife to cut two slashes on top.
Put the tray in the oven and immediately reduce the heat to 220° (430° F). Bake the turnovers for 10 minutes, then lower the heat to 200° (390°F). Bake for 10 minutes, then turn the heat to 180° (350°F). Continue to bake for five to 10 minutes, or until the turnovers are golden brown and fully cooked – they will be fragrant and firm, and will lift easily from the baking tray.
Cool the turnovers slightly before serving. Dust them lightly with icing sugar, then serve warm or at room temperature.