Whisk the flour, yeast, sugar, salt and lemon zest in a 4-quart / 3.8 L bowl. Add the lukewarm milk and egg and mix until shaggy. Knead on a lightly floured counter for 5 minutes, add the soft butter in three pieces, then knead 5 more minutes until the dough is smooth, slightly tacky and springs back when pressed.
Return the dough to the bowl, cover, and let it rise at about 24 C / 75 F for 60 minutes until doubled. While it rises, soak the raisins and chopped figs in the grappa and warm water for 15 minutes or longer, then drain well and pat dry on a towel.
Punch down the dough and flatten it into a rough 25 x 20 cm rectangle. Scatter the fruit, walnuts and chopped erba di San Pietro over it, fold the dough over, and knead for 1 minute, dusting with a little flour, until the fruit is evenly spread.
Butter a 23 cm / 9-inch springform pan and line the base with parchment. Shape the dough into a ball and press it edge to edge to a thickness of about 3 cm. Cover and let it rise for 40 minutes until puffy and slow to spring back when poked. Heat the oven to 180 C / 355 F for the last 15 minutes.
Brush the top with milk and sprinkle with coarse sugar. Bake for 35 minutes until deep golden and a thermometer in the center reads 93 C / 200 F. If the top is already dark at minute 25, tent it with foil.
Cool in the pan for 10 minutes, release the springform, and move the cake to a wire rack. Let it cool for 20 more minutes so the crumb sets, then cut into 10 wedges with a serrated knife.