Sprinkle 1 tablespoon sugar and the yeast into the lukewarm water and let stand until foamy, about 5 minutes. Using a standing mixer fitted with a paddle attachment, combine the flour, salt and baking powder at low speed.
In a medium bowl, stir together the buttermilk and 2 tablespoons melted butter. Add to the dry ingredients along with the yeast mixture and 3 tablespoons roasted garlic and mix at low speed until just combined. Switch to the dough hook and knead at medium speed until smooth, elastic and slightly sticky, about 5 minutes.
Grease a large bowl with 1 tablespoon melted butter and roll the dough in the butter to coat. Cover the bowl with plastic wrap and let rise until doubled in size, about 1 hour.
Meanwhile, in a medium saucepan, bring the tomatoes, vinegar, remaining 1/4 cup sugar and remaining roasted garlic to a boil, stirring constantly. Lower the heat and simmer until the chutney thickens, about 15 minutes. Season with salt.
Preheat a griddle or large, heavy skillet over medium heat. Place the dough on a work surface and cut into 8 pieces. Lightly flour the work surface and roll out 1 piece of dough into a 6-inch-long oval. Add to the hot skillet and cook, turning once, until puffed and golden, about 3 minutes total. Repeat with the remaining dough. Brush the flatbreads with the remaining melted butter and sprinkle with salt. Serve with the chutney.