Preheat the oven to 425 degrees. Toss the broccoli florets on a baking sheet with a drizzle of olive oil and a hefty sprinkling of kosher salt. Roast for 20 minutes.
While the broccoli is roasting, prepare the vinaigrette. Heat 1/4 cup of olive oil in a small skillet over medium heat until quite warm (about 2 minutes). Stir in the minced garlic and the smoked paprika and remove the pan from the heat. Let stand 10 minutes.
Put the sherry vinegar and a pinch of salt in a small bowl. Slowly whisk in the paprika oil. Try to leave most of the solids (paprika and garlic) in the skillet, if possible.
After 20 minutes, remove the broccoli from the oven and toss the almonds on top. Drizzle with a few tablespoons of the vinaigrette, toss, and serve immediately.