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1
Bring milk to boil in small saucepan or in bowl in microwave.
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2
In large, heavy-bottomed saucepan whisk together sugar, cornstarch, egg yolks, and salt until very thick and pale. While vigorously whisking, add 1/4 cup hot milk, then, add remaining milk in a slow steady stream, all the while whisking. (See Notes)
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3
Add cinnamon stick and bring the mixture to boil over medium-high heat, whisking constantly; mixture will thicken to the consistency of yogurt. Once custard has begun to boil, continue to boil for 1 to 2 minutes.
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4
Remove from heat and stir in butter and vanilla. Remove and discard cinnamon stick.
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5
Strain custard into large bowl and cool completely, at least 2 hours. To avoid a skin forming, press a piece of plastic wrap directly on the custard's surface. (See Notes).
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6
Adjust oven rack to middle position and preheat oven to 325u00b0F.
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7
Combine flour and baking powder in small bowl; set aside.
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8
In large, clean, dry bowl beat egg whites and salt with whisk attachment on medium-low speed until whites loosen and begin to froth, about 1 minute. Increase speed to medium-high and beat whites until soft peaks form, 1 to 2 minutes. Slowly add the sugar, a small amount at a time, and continue beating until stiff peaks form, 2 to 3 minutes.
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9
Add egg yolks and beat just until combined. Decrease speed to low and add flour in three batches, alternating with milk, scraping sides and bottom of bowl as necessary. Add vanilla and beat just until combined.
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10
Scrape batter into ungreased 9-inch round baking dish. Bake until cake tester inserted in center comes out clean, 30 to 35 minutes. Transfer cake to cooling rack and cool in pan completely, 1 to 2 hours.
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11
Poke cooled cake all over with skewer. Brush cake with 3/4 cup fig syrup.
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12
Top with custard and figs. Serve, passing additional fig syrup at table.
