Preheat a char-grill to high. Drizzle both sides of bread slices with olive oil, season to taste and char-grill, turning occasionally, until toasted and slightly charred on the edges (3-4 minutes), rub with cut side of garlic and set aside.
Drizzle asparagus with olive oil, season to taste and grill until tender and slightly blistered (2-3 minutes). Set aside.
Spread crostini with feta, top with asparagus, drizzle with extra olive oil and lemon juice and serve.