Cut in half lengthwise and scoop out seeds with a spoon. Meanwhile, peel 1 large English hothouse cucumber (about 12 oz.) in alternating stripes.
Bake, tossing halfway through, until crispy and golden brown, 25–30 minutes. Transfer quinoa to a baking sheet and toss with 2 Tbsp. Add ½ cup white, red, or tricolor quinoa, rinsed, then reduce heat to low and simmer, stirring occasionally, until quinoa is tender and most of the liquid is absorbed, 12–15 minutes.
Bring 2 cups water to a boil in a medium saucepan over high heat.