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Step 1
Season the steak heavily with salt and pepper. Let it sit for at least 10 minutes and up to 1 hour.
Step 2
Heat a heavy medium skillet over high heat. Blot off any excess moisture from the surface of the steak, add it to the skillet, reduce the heat to medium, and cook until the first side is nicely browned and the steak looks about one-third done.
Step 3
Flip the steak and cook until rare or medium-rare. The timing depends totally on the thickness and texture of your steak; a 1-inch filet mignon will take about 10 minutes total to get to medium-rare. Transfer to a plate to rest and tent with foil. Don't wipe out the skillet.
Step 4
Pile the broccoli florets and coins into the still-hot skillet, increase the heat to high, add 1/2 cup water, cover, and steam for 3 to 4 minutes. Uncover and cook until the broccoli is tender and the water has evaporated, another 3 to 4 minutes, depending on the size of your florets.
Step 5
Remove the pan from the heat, add 1/3 cup vinaigrette, and toss to combine. Taste and adjust with more vinaigrette, salt, or pepper.
Step 6
Slice the steak across the grain. Arrange the broccoli on a plate or platter, top with the steak and any accumulated juices, sprinkle the breadcrumbs over everything, and serve right away.
Step 7
Put the vinegar and raisins in a little bowl and let the raisins plump for about 30 minutes.
Step 8
Put the garlic in a food processor and pulse until finely minced, scraping down the sides of the bowl as needed.
Step 9
Add the capers and anchovies and pulse until you have a coarse paste. Add the parsley and pulse until completely chopped, again scraping down the sides of the bowl as necessary.
Step 10
Add the raisins and vinegar and pulse until the mixture is blended but still slightly coarse. Scrape the mixture from the processor into a bowl and whisk in the olive oil to make a slightly chunky dressing. Taste and adjust with salt or more oil, if needed. Store in the fridge for up to 3 weeks.