Preheat grill to medium-high.
Combine butter, basil, chives, parsley, lemon juice, thyme and 1/4 teaspoon each salt and pepper in a food processor. Pulse until well combined, scraping down the sides as necessary.
Brush steak with oil and sprinkle with 1/2 teaspoon salt and the remaining 1/2 teaspoon pepper. Grill the steak, flipping occasionally, until slightly charred and an instant-read thermometer inserted in the center registers 125 degrees F for medium-rare, 8 to 10 minutes. Transfer to a clean cutting board and let rest for 10 minutes. Spread 1 tablespoon of the herb butter on the steak.
Meanwhile, grill corn, turning occasionally, until slightly charred and tender, 6 to 8 minutes. Transfer to the cutting board. Spread the remaining herb butter on the corn.
Thinly slice the steak against the grain and sprinkle with the remaining 1/4 teaspoon salt. Serve the steak and corn sprinkled with feta and more parsley, if desired.