Heat the oven to 230 C / 445 F with a rack in the middle. While it heats, cut the cream cheese into 2 cm cubes and leave them on the counter to soften. If your eggs are cold, set them in a bowl of warm tap water for 5 minutes.
Crumple two 35 cm / 14-inch squares of parchment, then smooth them out and press them crisscrossed into a 20 cm / 8-inch springform pan. The paper should stand about 5 cm above the rim.
Beat the cream cheese and sugar in a 3-quart / 2.8 L bowl with a hand mixer on medium speed for about 2 minutes, until smooth with no visible lumps. Scrape down the bowl halfway through.
Sift the hojicha powder, flour and salt over the bowl. Mix on low speed for about 30 seconds, until no dry streaks remain.
Add the eggs one at a time, mixing on low for 20 seconds after each. Pour in the cream and vanilla and mix just until the batter is smooth and pourable, like a thick milkshake.
Pour the batter into the lined pan and tap it on the counter twice to release air bubbles. Bake for 35 minutes, until the top is deep brown with dark patches, the edges are puffed and set, and the center jiggles like gelatin when you nudge the pan.
Cool the cake in the pan on a rack for 60 minutes. It will sink in the middle as it cools. Remove the ring, peel back the parchment and serve slightly warm, or chill for 4 hours for firmer slices.