Preheat oven to 350°. Make cake: Butter a 9-in. round pan or 8 (1-cup) ramekins and line with parchment paper or waxed paper cut to fit. Butter the paper. In a bowl, toss rhubarb with 3 tbsp. granulated sugar. Spoon evenly into pan or ramekins; if using ramekins, set on a rimmed baking sheet.
Melt chocolate in a small metal bowl over a pan of barely simmering water, whisking until smooth, 2 to 4 minutes. Let cool.
Beat butter and 1/2 cup granulated sugar in a bowl with a mixer until fluffy. Add egg whites and vanilla and beat until well blended. Combine flour, baking powder, and salt in another bowl. Beat flour mixture into egg mixture half at a time, alternating with milk, until smooth. Stir in chocolate.
Spread batter evenly over rhubarb. Bake cake until golden brown and a toothpick inserted in center comes out almost clean, 28 to 35 minutes. Let cool in pan or ramekins about 30 minutes.
Make sauce: Heat cream and rosemary in a small saucepan over medium heat until bubbles form at edge of pan, stirring occasionally, 3 to 5 minutes. Remove from heat and discard rosemary.
Stir granulated sugar with lemon juice and 2 tbsp. water in a 12-in. frying pan. Cook over medium-high heat, occasionally picking up pan and swirling mixture around sides to wash down sugar crystals, until deep golden, 5 to 6 minutes. Immediately remove pan from heat, add cream (it will bubble up), and whisk until smooth. Scrape sauce into a serving bowl.
Make compote: In a small saucepan over medium heat, bring brown sugar, 1/3 cup water, and the rhubarb to a boil, stirring occasionally. Reduce heat and simmer until rhubarb is tender, 4 to 5 minutes.
Loosen cake from sides of pan or ramekins with a small metal spatula. Invert pan onto a platter (or invert ramekins onto dessert plates) and remove paper. For cake on platter, cut into wedges and transfer to plates. Using a slotted spoon, spoon compote and some syrup on cake. Spoon some sauce next to cake and serve the rest on the side. Serve with chamomile ice cream.
Note: Nutritional analysis is per serving.