1. Prepare Crostini: Preheat oven to 375°F (190°C). Arrange baguette slices on a baking sheet, brush lightly with olive oil, and bake for 7-10 minutes, until golden and crisp. While still warm, gently rub the surface of each toast with the cut side of the halved garlic clove. Set aside.

2. Prepare Beef: Pat the beef tenderloin dry with paper towels and season generously on all sides with kosher salt and freshly ground black pepper. Let it sit at room temperature for at least 30 minutes.

3. Grill Beef: Heat a grill or cast-iron skillet over high heat. Sear the beef for 3-5 minutes per side for a perfect medium-rare (internal temperature of 130-135°F). Remove from heat and let the meat rest on a cutting board for 10 minutes before slicing thinly against the grain.

4. Make Béarnaise Reduction: While the beef rests, combine the vinegar, shallots, and 1 tablespoon of the fresh tarragon in a small saucepan. Bring to a simmer and cook until the liquid has reduced by about two-thirds, down to about 2 tablespoons. Strain the reduction through a fine-mesh sieve into a heatproof bowl, pressing on the solids to extract all the liquid; discard the solids.

5. Make Béarnaise Sauce: Place the bowl with the reduction over a saucepan of gently simmering water (to create a double boiler). Add the egg yolks to the reduction and whisk vigorously and constantly until the mixture is pale, airy, and has thickened enough to leave ribbons when the whisk is lifted.

6. Emulsify the Sauce: Remove the bowl from the heat. Very slowly, in a thin stream, begin drizzling in the melted clarified butter while whisking constantly. Continue until all the butter is incorporated and the sauce is thick and creamy. Stir in the remaining 1 tablespoon of fresh tarragon and season with salt.

7. Assemble and Serve: Top each garlic crostini with a slice or two of the grilled tenderloin. Spoon a small amount of the warm Béarnaise sauce over the beef. Garnish with a final pinch of fresh tarragon if desired and serve immediately.