Preheat oven to 350°.
Toast juniper berries in a small skillet over medium heat until aromatic, 2–3 minutes. Let cool. Finely grind in spice mill.
Sift flour, sugar, cocoa powder, salt, baking soda, and ground juniper berries into a large bowl. Whisk buttermilk, oil, eggs, and 1 Tbsp. plus 1 tsp. water in a medium bowl. Whisk wet ingredients into dry ingredients. Pour batter into prepared baking dish; smooth top.
Bake cake until a tester inserted into the center comes out clean, 35–40 minutes. Let cool in pan on a wire rack. Cover and chill in freezer until frozen, about 2 hours. (Can be made 3 weeks ahead. Wrap in 2 layers of plastic; keep frozen)
Bring milk and sugar to a boil in a medium pot over medium heat, stirring to dissolve sugar (take care that milk doesn’t boil over). Reduce heat to low. Simmer gently, whisking occasionally, until milk is thick, turns light reddish-brown, and measures scant 1 cup, 40–45 minutes. Transfer jam to a heatproof jar; let cool. DO AHEAD: Can be made 1 week ahead. Cover; chill.
Unwrap cake and invert onto a work surface; discard parchment. Using a long serrated knife, trim cake to form clean edges. Cut cake in half lengthwise, then cut each half crosswise into 1 1/4-inch–wide bars.
Heat a nonstick skillet over medium heat. Pour a layer of sugar onto a plate. Roll each bar in sugar, coating completely. Working in batches, caramelize cake in skillet, turning with tongs to brown evenly, about 30 seconds per side per batch (be careful; the sugar burns quickly).
Whisk together 1 Tbsp. milk jam and crème fraiche in a small bowl. Add more milk jam to taste to sweeten, if desired. Serve warm, with Milk Jam Crème Fraîche.