Warm the milk to 45°C.
Combine salt, sugar, eggs, lime zest, flour, yeast, and 130ml water in a mixer bowl.
Slowly mix in the milk using a dough hook until a dough forms.
Mix on medium speed for three minutes then incorporate butter until smooth.
Cover and prove the dough in a warm place at 27°C for 45 minutes.
Purée 350g raspberries, 25g mint, and lemon juice in a processor.
Sieve the purée and weigh it into a pan.
Add an equal weight of sugar and heat gently until dissolved.
Add a knob of butter, bring to a rolling boil for four minutes, then cool.
Knock back the dough on a floured surface and fold a few times.
Roll dough to 1cm thick and cut using 9cm and 3cm cutters.
Place on greased trays, spray with oil, and prove for 20 minutes.
Heat oil in a deep fryer to 180°C.
Fry doughnuts in batches for three minutes until golden brown.
Cool doughnuts on wire racks with kitchen roll.
Inject jam into four points around each cooled doughnut using a piping bag.
Boil glaze ingredients together until sugar dissolves and cool slightly.
Brush the glaze evenly over the doughnuts.
Decorate each with four raspberry halves and mint leaves.