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Preheat oven to 375°F (190°C).
Brush baguette slices lightly with olive oil on both sides, season with a little salt and pepper.
Toast in the oven for about 8–10 minutes, flipping halfway, until golden and crisp.
Rub the beef with olive oil, salt, and pepper.
Grill (or sear in a hot pan) over medium-high heat for about 3–4 minutes per side for medium rare (depending on thickness).
Let it rest for 5–10 minutes, then slice thinly.
In a small saucepan, combine white wine vinegar, white wine, shallots, and half the tarragon.
Bring to a simmer and reduce to about 1 tbsp of liquid. Let it cool slightly.
In a heatproof bowl over a double boiler (or gently on low heat), whisk egg yolks with the reduction.
Slowly drizzle in the melted butter while whisking constantly until thickened.
Stir in remaining tarragon, season with salt and pepper.
Place a beef slice on each toasted crostini.
Spoon a dollop of Béarnaise sauce on top.
Garnish with extra chopped tarragon or microgreens if desired.