Preheat grill to medium-high.
Brush pork with 1 tablespoon oil and sprinkle with 1 teaspoon thyme, chile powder and ½ teaspoon salt.
Grill, flipping occasionally, until an instant-read thermometer inserted in the thickest part registers 145 degrees F, 14 to 20 minutes.
Transfer the pork to a cutting board and let rest for 5 minutes.
Meanwhile, heat the remaining 1 tablespoon oil in a medium skillet over medium heat.
Add shallots and the remaining 1 teaspoon thyme and cook, stirring occasionally, until softened, about 2 minutes.
Add cherries and cook, stirring occasionally, until the cherries are softened, 3 to 6 minutes.
Stir in wine and increase the heat to high; cook for 1 minute.
Remove pan from heat and stir in basil and the remaining ¼ teaspoon salt.
Slice the pork and stir any juices into the cherries.
Serve the pork with the cherries. Garnish with more basil, if desired.
