Preheat oven to 450 deg. Place currants in small bowl with 2 Tbsp warm water to plump.
Place squash on sheet pan; drizzle with 1 tsp olive oil; season with salt and pepper. Roast, cut side down, 20 min or until tender when pierced by a fork. Remove from oven and flip to cut side up.
Cook farro in a med pot of boiling salted water, uncovered, 16 min or until tender. Drain; return to pot.
In skillet heat 1 tsp olive oil. Add mushrooms and cook, stirring occasionally, 5 min. Season with salt and pepper; cook until softened. Transfer to a plate. In the same pan, heat 1/2 tsp olive oil; add leek and garlic; season with salt and pepper. Cook 3 min, stirring occasionally. Add mushrooms, thyme, and vinegar; season with salt and pepper, cook 1 min more. Turn off heat and add drained currants.
Combine farro and vegetables. Add Fontina and 1 1/2 tsp olive oil, season with salt and pepper.
Tightly pack each squash half with filling; drizzle on 1 tsp olive oil. Top with Parmesan; bake 5 min or until cheese melts. Remove from the oven; rest 2 min. Garnish with parsley.