Preparation Preheat oven to 375°F with rack in middle. Pat pork dry and sprinkle with 3/4 teaspoon salt and 1/2 teaspoon pepper. Heat vegetable oil in a 12-inch ovenproof heavy skillet over medium-high heat until it shimmers, then brown pork on all sides, about 6 minutes total. Transfer pork in skillet to oven and roast until an instant-read thermometer inserted into center registers 145 to 150°F, 20 to 25 minutes. Transfer to a cutting board and let stand 10 minutes. While pork stands, add vinegar to skillet (be careful; handle will be very hot) and boil, scraping up any brown bits, until slightly reduced, about 30 seconds. Transfer to a heatproof measuring cup and add enough olive oil to bring total to 3/4 cup liquid. Pulse 3/4 cup walnuts with garlic, water, 1/2 teaspoon salt, and 1/4 teaspoon pepper to a coarse paste in a food processor. With motor running, slowly add oil mixture to make vinaigrette. Toss arugula and endive with just enough vinaigrette to coat, then divide among plates. Top with thin slices of pork and drizzle with remaining vinaigrette. Crumble remaining 1/4 cup walnuts over pork.
Preparation Preheat oven to 375°F with rack in middle. Pat pork dry and sprinkle with 3/4 teaspoon salt and 1/2 teaspoon pepper. Heat vegetable oil in a 12-inch ovenproof heavy skillet over medium-high heat until it shimmers, then brown pork on all sides, about 6 minutes total. Transfer pork in skillet to oven and roast until an instant-read thermometer inserted into center registers 145 to 150°F, 20 to 25 minutes. Transfer to a cutting board and let stand 10 minutes. While pork stands, add vinegar to skillet (be careful; handle will be very hot) and boil, scraping up any brown bits, until slightly reduced, about 30 seconds. Transfer to a heatproof measuring cup and add enough olive oil to bring total to 3/4 cup liquid. Pulse 3/4 cup walnuts with garlic, water, 1/2 teaspoon salt, and 1/4 teaspoon pepper to a coarse paste in a food processor. With motor running, slowly add oil mixture to make vinaigrette. Toss arugula and endive with just enough vinaigrette to coat, then divide among plates. Top with thin slices of pork and drizzle with remaining vinaigrette. Crumble remaining 1/4 cup walnuts over pork.