Preheat oven to 350 degrees. Grease two 6-slot doughnut pans with oil.
In a large bowl, beat together the melted butter, sugar, and yogurt until smooth. Whip in the eggs, one at a time, then the vanilla. Scrape down the sides of the bowl with a spatula. Add the flour, baking powder, baking soda, salt, cinnamon, cardamom, ginger, cloves, and black pepper. Beat until just combined. Slowly stream in the buttermilk until smooth. Fold in the blueberries, then the blueberry jam. Try to preserve some streaks of jam in the batter if you can.
Snip the tip of a gallon freezer bag and fill with the batter. Carefully pipe the batter into each doughnut slot, filling only 3/4 of the way. Bake 12-15 minutes until firm and an inserted toothpick emerges with only a few moist crumbs. Cool 5 minutes in the pan, then move to a wire rack. Cool completely.
In a small bowl, whisk together the powdered sugar, lemon juice and zest, and vanilla. If the glaze seems too thick, add 1 tablespoon of milk at a time until desired consistency is reached.
Slide a piece of parchment paper beneath the cooling rack to catch drips. Dunk each doughnut in the glaze, twirling to remove excess glaze, and set unglazed-side down on the rack. Serve with coffee or tea.