Start by cooking the apples: peel and chop them to about 1cm dice. Place in a pan over a medium flame with the butter and cinnamon. Add some water and cook until soft. Set aside.
In a large bowl, using an electric/stand mixer (or hand whisk, just double/triple the times) combine the butter and both sugars on medium speed for several minutes, until fully combined. Add the egg and vanilla and mix again.
Add the flour, baking powder and cooked apples. Fold until combined. The dough should be fairly solid at this stage (it ought to almost form a ball, albeit a very soft one!). Cover and chill for at least 30 minutes.
Preheat the oven to 200C/180C Fan/Gas 6. Line 2-3 large baking trays.
Roll into about 10 balls (use a tablespoon to scoop balls of dough). Place on lined baking sheets.
Make the streusel: use a fork to mash the butter into the sugar, oats and flour until sand-like in texture.
Roll the cookie dough into about 10 balls (use a tablespoon to scoop balls of dough) and place on lined baking sheets, pressing down a little. Add on the streusel/crumble and pat down.
Bake 10-12 minutes, until golden and just crisping up at the edges (they continue to cook a little once removed). Let cool on a wire rack.