Place shallots in a small nonreactive bowl. Bring vinegars, sugar, and 1 cup water to a boil in a small saucepan, stirring to dissolve sugar.
Pour over shallots; chill.
DO AHEAD: Shallots can be pickled 5 days ahead. Cover and keep chilled.
Heat oil in a medium skillet over medium-high heat.
Add onion, season with salt, and cook, stirring often, until soft, 5-7 minutes.
Add wine, vinegar, sugar, cinnamon, star anise, red pepper flakes, and allspice. Bring to a boil, reduce heat, and simmer, stirring occasionally, until liquid is thickened and syrupy, 40-45 minutes.
DO AHEAD: Jam can be made 5 days ahead. Cover and chill.
Heat oil in a large pot over medium-high heat.
Add onions, leek, celery, garlic, chile, and ginger; season with salt. Cook, stirring often, until soft (do not let brown), 10-12 minutes.
Add wine and mirin to pot, bring to a boil,and cook until reduced by half, about 4 minutes. Reduce heat to medium, cover, and cook, stirring occasionally, until onions are soft and translucent, 25-30 minutes.
Let cool slightly, then purée in a blender until smooth. Strain into a large bowl and stir in cream (thin with water, if needed); season with salt. Reheat soup in a clean pot.
DO AHEAD: Soup can be made 2 days ahead.
Let cool; cover and chill.
Heat butter in a large skillet over medium heat. Cook bread until golden, about 3 minutes (you'll have 2 extra). Flip, top with cheese, cover, and cook until cheese is melted, about 4 minutes. Top toasts with pickled shallots and chives.
Spoon some jam into each bowl, pour soup around, and top with toasts.