Preheat the oven to 375°. Set the broccoli on a cutting board, stem side up. Slice vertically into ½-inch slabs. Some of the florets will fall off — set those aside and store for another use. Lay the slabs on a baking sheet. Do not use parchment paper or a silicone mat, as this will prevent browning. Using a pastry brush, generously oil the broccoli. Sprinkle with salt, pepper and garlic powder. Roast for 25 minutes, or until slabs are generously browned and stems are tender.
While broccoli is roasting, combine shallot, garlic, vinegars, water, mustard and salt in a mason jar. Allow to sit for 15 minutes as the shallot mellows in the vinegar. Add oil, secure jar with lid and shake until oil is emulsified, about 30 seconds. Stir in capers.
To serve the broccoli, spoon caper vinaigrette over steaks and garnish with pine nuts and grated cheese.