Step 1 Cut off the stem top and the root bottom of the onion and discard. Slice the onion in half from the stem top down. Put each half flat-side down on a cutting board. Slice the onion in 1/4 inch vertical slices. Holding the half together slice the half into 1/4 inch slices horizontally. Then cut across the onion vertically, making a 1/4-inch dice. Put the onion pieces aside.
Step 2 Break off the stems and slice the mushroom caps into 4 pieces. Add the pieces with the mushroom stems and set aside.
Step 3Melt the shortening over medium heat in a heavy Dutch oven or large heavy pot with a lid. Add the chopped onion and cook until the onion is light golden, 6 to 8 minutes, stirring occasionally, so it doesn't get too browned. Remove the onion and set aside.
Step 4Mix the flour, salt and pepper on a dinner plate and roll the meat in the mixture. Brown the beef over medium-high heat, a few pieces at a time in the Dutch oven, moving them around so all sides get brown. When all the beef chunks are browned and in the pot, add the marjoram, thyme, wine and water or beef broth. Return the onion to the pot, cover, and reduce the heat to simmer. Simmer for 1 1/2 hours, checking to make sure there is still liquid in the pot. Add a little more water or broth if needed. Add the boiling onions and cook 20 minutes, then add the mushrooms and cook 10 minutes more. Taste and add more salt and pepper if needed. When the onions are fork-tender, the stew is done.