Cover the soaked beans with 2-inches of water. Bring to a boil and reduce to aa rapid simmer. Let cook for 35 minutes.
Pour in the olive oil and red wine vinegar. Add the oregano, crushed pepper flakes, and pepper. Stir to combine. Cover and transfer the beans to the refrigerator. Let marinate for at least 1 hour.
Mash the salt, anchovy and garlic together. Add the yolk, mustard, and lemon juice. Whisk the olive oil in in small increments. Repeat with the neutral oil.
Pour a tablespoon of the olive oil onto a large baking sheet. Use a pastry brush to evenly distribute the oil. Arrange the bread on top.
Drizzle the bread with another tablespoon of oil and sprinkle with salt. Bake the croutons on the middle rack for 15 minutes
Place the asparagus, oil, and salt in a bowl. Toss to coat. Heat a large cast-iron griddle until smoking. Grill until tender and nicely charred.
Place the kale in a large salad bowl. Add the dressing and toss to coat. Transfer the kale to a platter and top with the white beans, asparagus, and croutons.