Preheat grill over medium-high heat. Brush corn and lime halves with vegetable oil. Season with salt and pepper.
Grill corn and limes 3-4 minutes per side. 10-12 minutes for the corn; 6-8 minutes for the limes. Remove from heat and tent with foil to keep warm.
When cool enough to handle, cut kernels from corn cobs. Transfer to a large bowl, and add red onion, poblano pepper, and jalapeño if desired. Squeeze in juice of grilled lime.
Add olive oil, cotija cheese, and season to taste with salt and pepper. Garnish with chives and parsley.
Serve warm or at room temperature. (Can be made 1 day ahead. Cover and chill. Let come to room temperature before serving.)
Notes
*You can substitute parmesan or manchego cheese for cotija if not available.