For the Chutney
In a medium pot combine all chutney ingredients. Stir and bring to a boil. Simmer, stirring occasionally until thick and cooked through, about 15–20 minutes.
For the Steak
Pat steak dry with a clean paper towel and season with salt and pepper.
Bring a cast iron skillet to medium-high heat and add 1 Tbsp. of olive oil.
Add steak to the pan and cook for 3 minutes, then flip. Continue cooking 2–3 minutes per side, and flipping, until internal temperature has reached 125–130 degrees F (medium rare).
Remove and let rest for about 10 minutes. Slice thin and set aside.
For the Crostini
Heat oven to 400 degrees F. Place baguette slices on a parchment-lined baking sheet and brush with a little olive oil.
Bake until light golden brown, about 8–10 min. Pull baking sheet from oven and put a slice of Mozzarella on each slice.
Return to oven and bake a few minutes more, until cheese is melted. Remove from oven and place crostini on a serving tray.
Top each with a pinch of arugula, a piece of steak, and 1 tsp. of chutney. Season with salt and pepper and serve.
For a crisp bite and a quick melt, toast the baguette slices until they are lightly golden before topping with the Mozzarella slices.