Wash each squash. Place whole squash in oven for about 45 minutes at 350F or until it punctures with a sharp knife. Let sit for a few minutes. Using oven mitts to hold the squash, cut a 3- to 4-inch circle around the top stem (opposite flat end). Save cut end for bowl lid.
To peel pearl onions:.
Place in boiling water for 2 to 5 minutes; blanch lightly. Remove from boiling water. Chop off end of pearl, and squeeze flesh out of skin.
In a Dutch oven, brown meat, in 2 Tbsp oil. Add water, dried mushrooms, potatoes, carrots, garlic, onions, and pepper. Cover and simmer for 2 hours.
Stir in bouillon and tomatoes. Remove squash 'lid' and set aside; discard seeds and loose fibers from inside. Place squash in a shallow baking pan.
Spoon stew into squash and replace the lids. Brush the outside of the squash with the remaining oil. Bake at 350 degrees F for 1/2 hour or until the squash is tender (do not over bake).