Preheat the oven to 425°F/220°C. Grease a doughnut pan.
In the bowl of a stand mixer with the paddle attachment, beat the butter, vegetable oil and sugars together until smooth, about 2-3 minutes. Add the eggs and beat to combine.
Add in the baking powder, baking soda, salt, nutmeg and vanilla and beat again to combine.
Pour the flour into the batter alternatively with the milk, starting and ending with the flour. You'll know the batter is ready when a spatula leaves a deep furrow when you pull it through the batter.
Pipe the batter into the doughnut pan, filling it up almost to the top and leaving about ¼ inch.
Bake the doughnuts for 10 minutes. They should be a light golden colour and spring back when you touch them. Let them cool in the pan for 5 minutes before taking them out and letting them cool on a rack.
Make Raspberry Glaze
In a small saucepan, cook the raspberries on a medium heat until the fruit begins to break down. While the berries are cooking, use a heatproof spatula to press the berries against the sides of the saucepan. Let the mixture boil for about 3 minutes.
Take a heatproof bowl and pour the raspberry juice through a fine-mesh sieve to remove the seeds. Let it cool.
In the same bowl, whisk together the raspberry juice, salt, vanilla and lemon juice. Pour in the icing sugar bit by bit until you have the consistency you want.
Dip each cooled doughnut into the glaze, let dry for 20 minutes.