Heat oil, garam masala, and garlic in a small saucepan over medium-high until fragrant, about 2 minutes.
Remove from heat and whisk in lemon juice, vinegar, and honey. Season vinaigrette with salt and pepper; set aside.
Toast pistachios in a small skillet over medium-low heat until golden brown, about 4 minutes. Transfer to a cutting board and let cool; finely chop.
Toss pistachios, shallot, jalapeño, broccoli, cilantro, and dates in a medium bowl. Drizzle dressing over and toss to coat. Taste and season with more salt and pepper if needed.