Trim the lemongrass down to the pale bottom third, peel off the woody outer layer, and mince it as finely as you can. Big pieces of lemongrass eat like splinters.
Mix the lemongrass, garlic, shallot, fish sauce, brown sugar, oil, lime juice, and pepper. Coat the thighs and marinate at least 30 minutes at room temperature, or up to 24 hours in the fridge.
Heat a grill pan over medium-high until properly hot. Lay the thighs flat and cook 5 to 6 minutes per side until charred in spots and cooked through (74C or 165F inside). Work in two batches rather than crowding the pan.
No grill pan? Broil on a foil lined tray, 8 to 10 cm from the element, about 6 minutes per side.
Rest 5 minutes, slice against the grain, and serve with rice, cucumber, cilantro, and lime wedges.