For the pork tenderloin:
Heat the oven to 400°F.

• Pat the pork dry with a paper towel. Season generously with salt and pepper.

In a large ovenproof frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the pork and cook, turning once, until lightly browned but not yet cooked through, 2 to 3 minutes per side. Transfer the pan to the oven and roast, turning once, until cooked through but still faintly pink within, 12 to 15 minutes. Transfer to a cutting board to rest for 5 minutes, then cut into ½-inch-thick slices. Do not clean the pan.
While the pork cooks and rests, prepare the caraway cabbage.

For the pork loin chops:

• Pat the pork dry with a paper towel. Season generously with salt and pepper.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the pork and cook, turning frequently, until browned but still faintly pink within, 8 to 10 minutes. Transfer to a cutting board to rest for 5 minutes, then cut into ½-inch-thick slices. Do not clean the pan.
While the pork cooks and rests, prepare the caraway cabbage.

• Cut away any core from the cabbage; cut the cabbage into 1-inch-thick slices.
• Cut the apple lengthwise into quarters and cut away the core; cut each quarter lengthwise into 1-inch-thick slices, then crosswise into 1-inch cubes.

In another large frying pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Working in batches if needed, add the cabbage and apple, season with salt and pepper, and cook, stirring occasionally, until starting to soften and brown, 2 to 3 minutes. Stir in the caraway seeds and cook until fragrant, about 1 minute. Remove from the heat and season to taste with salt and pepper.
While the cabbage and apple cook, prepare the fig agrodolce.

• Trim the stems from the figs; coarsely chop the figs.
• Peel and thinly slice the shallots.
• In a small bowl, using a whisk, mix together the figs, balsamic vinegar, arrowroot powder, 2 tablespoons [¼ cup] water, and 1 teaspoon [2 tsp] oil.

In the same pan used for the pork (being careful of the hot handle), warm 1 to 2 teaspoons oil over medium-high heat until hot but not smoking. Add the shallots, season with salt and pepper, and cook, stirring occasionally, until starting to soften, 2 to 3 minutes. Stir in the fig-balsamic mixture and cook, whisking constantly, until the sauce is thickened, about 30 seconds. Remove from the heat and season lightly to taste with salt and pepper.

Transfer the caraway cabbage to individual plates. Top with the pork, spoon over the fig agrodolce, and serve.