In a 12-inch skillet over medium heat, cook the pancetta in the olive oil, stirring frequently, until the pancetta has rendered much of its fat and is nicely browned, 4 to 5 minutes. Increase the heat to medium high, stir in the carrot, shallot, and red pepper flakes and cook to soften the vegetables, 1 to 2 minutes. Add the sprouts, season lightly with salt and pepper, stir to coat with the fat, and cook, stirring, until the sprouts wilt slightly and a few brown lightly, 2 to 3 minutes.
Add the broth and thyme, cover with the lid slightly ajar, and adjust the heat to a lively simmer. Cook the sprouts until they’re just barely tender, 4 to 6 minutes. Remove the lid, increase the heat to medium high and cook, stirring frequently, until all the liquid has evaporated and the sprouts are quite tender (but not mushy), about 3 minutes. Off the heat, gently stir in the sun-dried tomato, butter, and lemon zest. Season to taste with salt and pepper.