Combine goat cheese, lemon juice, extra virgin olive oil, salt, pepper, and red pepper flakes in a food processor. Pulse until goat cheese is whipped and creamy. Add whipped goat cheese to a large plate or serving tray and set aside.

Bring a large pot of salted water to a boil. Add broccolini and cook until bright green, about 3-5 minutes. Remove broccolini from water and set aside.

Heat olive oil in a large skillet over low heat. Add shallots and cook until crispy, about 8-10 minutes. Add garlic, red pepper flakes, salt, and pepper and stir well. Remove from heat.

Top plated whipped goat cheese with broccolini and pour crispy shallots and remaining oil over broccolini.

Garnish with lemon wedges and fresh basil.