Cut off the skin of the squash and scoop out the seeds. Cut into wedges.
Peel the potatoes (or not) and cut into wedges.
Place the vegetables in a large cooking pan and add about 2 cups of water. Simmer, preferably with ham or meat bones, for 20 to 30 minutes or until very tender. There should be very little liquid by the time the vegetables are done.
While the vegetables simmer, melt the butter in a small saucepan. Add the minced garlic and chopped onion and cook gently until soft. Keep warm.
Drain the squash and potatoes, place in a large bowl and mash with a fork or a potato masher. Add the garlic and onion, with the butter, and season with salt and pepper. Stir until blended. Pour in the milk, little by little, stirring to combine. Stop adding milk once you have reached the desired consistency which, ideally, means soft but still able to hold shape.