Bring a large pot of salted water to boil.
Take half of a butternut squash (innards removed) and microwave it in a microwave safe bowl for 5 minutes, check for doneness (a fork should poke easily through) and continue cooking in 1-2 minute intervals, checking in-between, until done. Remove the butternut squash from the microwave, and carefully remove the skin. Scrape the contents of the butternut squash into a food processor.
Into the food processor add 1 cup of flour, and 1/2 cup of the wheat flour, the milk, nutmeg, salt and pepper. Process until smooth, then add the remaining 1/2 cup of ap flour and 1/2 cup of whole wheat flour. Process the dough. The gnocci dough should be sticky, but not liquidy. If the dough is too soft, add a little bit more flour and process. The denser your dough, the denser your gnocchi will be.
Carefully transfer gnocchi dough from the food processor onto a flour dusted cutting board. Divide the dough into four equal parts and then roll them into long rows.
Cut each row into little pieces.
When the water is boiling, add the cut pieces (the gnocchi) into the water carefully using a slotted spoon.
Let the gnocchi boil until they float to the top, then carefully remove them with a slotted spoon.
Once all the gnocchi are done being boiled, return them to the pot and add the butter in to melt it over the gnocchi and sprinkle with cheese.