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In a large bowl, rub together the flour, butter, mustard powder, cayenne, polenta (if using), poppy seeds, stilton and a pinch of salt, using your fingers and hands, until the mixture forms a pastry dough. Knead the dough briefly until it really sticks together and is very lightly speckled with tiny bits of cheese. You can be quite heavy-handed.
On a lightly floured surface, roll the dough into a sausage shape with your hands, about 25cm long and 4cm in diameter, then wrap in cling film and chill for at least 1 hour. (The pastry can now be chilled for up to 1 week or frozen for up to 1 month. The pastry can be sliced and cooked from frozen but you need to cut it slightly thicker.)
To bake the biscuits, preheat the oven to 190C/gas 5/ fan 170C. Slice the dough into rounds just under 1cm thick. Lay the rounds a couple of centimetres apart on a baking sheet (or two, if you are cooking all the biscuits at the same time). Put a very small piece of stilton in the middle of each biscuit, then bake for 10-15 minutes, until the edges are starting to go golden and the cheese is bubbling. Leave to cool slightly before serving. The biscuits will keep for 2-3 days in an airtight tin.