Heat the oven to 400F.
Place the green beans and shallots on a large, rimmed baking sheet. Drizzle with 1 tablespoon olive oil, sprinkle with ¼ teaspoon salt, and toss to combine.
Place the brussels sprouts on a second large, rimmed baking sheet. Drizzle with 1 tablespoon olive oil, sprinkle with ¼ teaspoon salt, and toss to combine.
Put the green bean and shallot pan on the top shelf of the oven, and the pan with the brussels sprouts on the bottom shelf. Roast for 15 minutes, remove the pans from the oven, stir the vegetables on each pan, then place the pans back in the oven on alternate racks (green beans and shallots on the bottom rack, brussels sprouts on the top).
Roast an additional 15 minutes, then remove from the oven. Stir the brussels sprout and return from the oven for an additional 15 minutes, until browned and crispy (about 30 minutes total for the green beans, 45 minutes for the brussels sprouts.)
Remove the brussels sprouts from the oven. Add the green beans and shallots to the brussels sprouts pan.
Drizzle with an additional 1 tablespoon olive oil and lemon juice, stirring to combine.
Spoon the brussels sprouts, green beans, and shallots to a platter. Sprinkle with pecans and cranberries. Taste and add additional salt or lemon juice if you like.
Serve warm or at room temperature.