Add the fresh corn kernels and water to a high-speed blender. Blend on high for about 5 minutes, or until completely smooth.
Pour the blended corn through a fine mesh strainer, pressing firmly to extract as much liquid as possible. Reserve the corn milk for the French toast custard and corn cream. Discard the pulp or save it for breads, fritters, or other recipes. Refrigerate the corn milk for up to 3 days if making ahead.
Whisk together the corn milk and eggs until completely smooth to create the French toast custard.
Arrange the thick slices of shokupan or brioche in a shallow dish and pour the custard over the bread. Gently press and squeeze the bread so it absorbs as much custard as possible, including the center.
Heat 1 tablespoon of butter in a cast iron skillet over medium heat. Add the soaked bread and cook until deeply golden on the first side.
Flip the French toast and place a press or heavy pan on top. Add the remaining tablespoon of butter, fresh thyme, and freshly ground black pepper to the skillet. Continue cooking until the second side is golden and crisp.
Remove the press and cover the French toast with freshly grated Parmesan. Transfer the skillet to a 350°F oven and bake for 8 to 10 minutes, or until the cheese is melted, bubbling, and deeply golden.
While the French toast bakes, heat the algae oil or neutral oil in a skillet over medium heat. Add the shallots and cook until softened, then stir in the fresh corn kernels and cook until lightly charred. Add the thyme leaves.
Push the vegetables to one side of the pan. Add the brown mustard seeds with a small drizzle of oil and toast until they begin to pop. Stir everything together.
Add the halved Bing cherries, butter, apple cider vinegar, kosher salt, and black pepper. Cook just until the cherries begin to soften while still holding their shape. Taste and adjust seasoning.
To make the corn cream, bring the remaining corn milk to a gentle simmer and cook until it naturally thickens. Stir in the chopped scallions and season with kosher salt.
Place the Parmesan French toast onto serving plates. Spoon the warm cherry mostarda over the top, then finish with generous spoonfuls of the hot corn cream.
Serve immediately.