Preheat oven to 350°.
Combine 1 cup hot water and porcini mushrooms in a small bowl; let stand 10 minutes. Drain mushrooms through a fine sieve into a bowl, reserving liquid. Chop mushrooms; set aside.
Sprinkle 1/2 teaspoon salt and pepper over ribs; dredge ribs in flour. Heat oil in a large Dutch oven over medium-high heat. Add ribs to pan; cook 12 minutes, browning on all sides. Remove ribs from pan. Add porcini mushrooms, cremini mushrooms, and next 4 ingredients (through garlic) to pan; cook 12 minutes or until mushrooms are tender. Add wine, scraping pan to loosen brown bits. Add mushroom liquid and broth; bring to a boil. Add ribs to pan; cover. Place pan in oven; bake at 350° for 2 1/2 hours or until ribs are tender. Let stand 10 minutes. Remove meat from bones; discard bones, fat, and gristle. Shred meat with 2 forks; return meat to pan. Stir in remaining 1/4 teaspoon salt. Cool completely. Place mixture in an airtight container or heavy-duty zip-top plastic bag; freeze.
Thaw meat mixture overnight in refrigerator. Place mixture in a large saucepan over medium heat; cook until thoroughly heated, stirring frequently.