Add the cannellini beans, garlic, olive oil, and chopped parsley to the bowl of a food processor. Blend until the mixture becomes smooth and creamy, pausing to scrape down the sides as needed so everything is evenly incorporated. Taste and season with sea salt and freshly cracked black pepper, adjusting the seasoning until the bean spread is well balanced and flavorful.
Pat the beef tenderloin dry with paper towels, then brush it lightly all over with olive oil. Generously sprinkle the meat with sea salt and black pepper, pressing the seasoning gently into the surface so it adheres.
Heat a grill pan or skillet over medium-high heat, or prepare a grill. Once hot, cook the beef tenderloin, searing it on all sides until it reaches your preferred level of doneness. Let the meat rest for several minutes so the juices redistribute, then slice it very thinly against the grain for tender, delicate pieces.
Arrange the Crostini Toasts on a serving platter. Spread a generous layer of the cannellini bean mixture over each toast, creating a smooth base that reaches close to the edges.
Place one or two thin slices of beef tenderloin on top of each crostini. Lightly brush the tops with a little extra olive oil to add sheen and richness, then finish with a final sprinkle of sea salt and freshly cracked black pepper to brighten the flavors.
Serve the Beef Tenderloin Crostin immediately as a refined appetizer or party bite, while the bread is crisp, the bean spread is creamy, and the beef is tender and succulent.