Heat a skillet over medium-heat and pour in the olive oil. Add the mushrooms and thyme and cook until browned all over.
Add the garlic, season with a good pinch of salt and pepper, then add the cream and cook until glossy and thickened.
Heat a second skillet over high heat (open the windows and turn on the fan. Trust.). Season the steak well with salt and pepper.
Add the neutral oil to the pan, then cook the steak, turning every 2 minutes for 8 minutes.
Add the butter, then baste until the the internal temperature of the steak reads 125 degrees F for a beautiful medium-rare (cook longer if preferred).
Let rest at least 10 minutes, then carve into thin strips.
Top toasted baguette with spoonfuls of burrata, a drizzle of olive oil, mushrooms, steak, chives, and basil.
