Heat olive oil in a large pan or skillet over medium-high heat.
Season chicken thighs all over with basil, paprika, salt and pepper, then place in skillet and cook for 5-7 minutes, or until browned. Flip over and brown the other side until chicken is cooked through.
Transfer chicken to a separate plate and set aside.
Heat butter in hot skillet and sauté garlic and basil for 1 minute, stirring frequently, until fragrant. Stir in flour and cook for another 1-2 minutes, or until golden.
Whisking continuously, pour in evaporated milk and bring to a boil.
Reduce heat and let mixture simmer, then return chicken to skillet and add broccoli florets. Stir everything together, then cover and cook for 3-5 minutes, or until broccoli is tendercrisp.