Vigorously whisk eggs, egg yolks, salt, white sugar, and brown sugar together in a large bowl until mixture turns light and frothy, about 1 minute. Add vanilla, cinnamon, lemon zest, milk, and cream; whisk to combine. Toss in bread slices and press down until they start to soften and are submerged. Let sit, pressing down occasionally with a spatula, until custard has been absorbed, about 20 minutes.