Combine flour, sugar, yeast, thyme, salt and cheeses in a large bowl. If you have a stand mixer, use your largest mixer bowl (then you can use your dough hook instead of hand kneading).
Place milk and butter in a medium saucepan. Warm gently until butter melts, should be tepid in temperature. Whisk 1 egg in to the butter/milk mixture.
Make a well in the centre of the flour mixture and add milk. Stir until combined and then turn dough out onto a floured surface and knead for 10 minutes until smooth. Alternatively mix dough on your stand mixer using dough hook until mixture is smooth.
Place dough in lightly oiled bowl, cover with plastic wrap and stand in warm place for 40 minutes or until doubled in size.
Knock back dough and cut into 12 (or 16 for smaller buns) equal pieces. Knead each piece in to a ball, place in a lightly greased lamington tin.
Cover with a damp tea towel and stand in a warm place for 40 minutes or until doubled in size.
Preheat oven 220 degrees C.
Cut your prosciutto in thirds length wise, then cut strips in half.
In a small bowl whisk egg and water to make egg wash.
Brush buns liberally with egg wash. Take two strips of prosciutto and place on top of bun to form a cross.
Place buns in oven and bake for 10 minutes. Then reduce temperature to 200 degrees C and bake for another 20 minutes until golden. When buns are ready they will sound hollow when tapped.
Remove from tray and allow to cool on wire rack or serve immediately.