Lightly coat ramekins with cooking spray.

In a heavy medium saucepan, dampen 1/3 cup sugar with 2 1/2 tablespoons water. Bring to a boil over medium heat, gently stirring until sugar is dissolved. Boil, without stirring but washing down any sugar crystals with a pastry brush dipped in cold water as necessary, until syrup begins to turn golden. Continue to boil, swirling pan occasionally, until syrup is a deep golden caramel. Immediately divide caramel among ramekins, tilting if necessary to coat bottoms.

In a medium saucepan, bring milk, 1/2 cup cream and cinnamon just to a boil. Remove pan from heat, cover and let stand 10 minutes. Meanwhile, in a large saucepan, combine 1/3 cup sugar, chocolate and polenta.

Remove and discard cinnamon from hot milk mixture, then, whisking constantly, pour over polenta mixture. Bring mixture to a bare simmer over very low heat; cook, whisking initially to dissolve any lumps, then stirring frequently with a wooden spoon, until polenta is thickened and tender, about 20 minutes; remove from heat and cover to keep warm.

In a bowl, beat together remaining 1/4 cup cream, egg and egg yolk. Add to polenta; return to heat and gently simmer, stirring constantly, 2 minutes. Immediately divide hot polenta mixture among prepared ramekins, pressing mixture firmly into molds to release any air bubbles, then cover ramekins with plastic wrap and chill until pudding is set, about 4 hours or up to 2 days.

Secure 1 lemon half onto the tines of a fork, with cut side facing out. In a heavy medium saucepan, dampen remaining
1/3 cup sugar with 2 1/2 tablespoons water. Bring to a boil over medium heat, gently stirring until sugar is dissolved. Boil, without stirring but washing down any sugar crystals with a pastry brush dipped in cold water as necessary, until syrup begins to turn golden. Continue to boil, swirling pan occasionally, until syrup is a deep golden caramel.

In a slow and steady stream, add orange juice, then stir with lemon half until clumps are dissolved into the caramel. Add maraschino and Cognac. Remove pan from heat and ignite alcohol with a match. Return pan to heat. When flames subside, add chestnuts. Very gently simmer 10 minutes, stirring occasionally, then remove pan from heat and let stand 10 minutes.

Run a thin knife along sides of ramekins to loosen, then invert budini onto serving plates. Spoon caramelized chestnuts over the top. Serve immediately.