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.