Bring 2 quarts water to boil in a medium saucepan over high heat. Add potatoes and carrot and cook until tender, about 12 minutes; drain in a colander.
Combine cooked vegetables, ⅓ cup water, 2 tablespoons oil, nutritional yeast, vinegar, and salt in a blender. Pulse until chopped and combined, about 10 pulses, scraping down sides of blender jar as needed. (You will need to stop processing to scrape down sides of blender jar several times for mixture to come together.) Process mixture on high speed until very smooth, about 2 minutes.
Meanwhile, heat remaining 1 tablespoon oil in the now-empty saucepan over medium-high heat until shimmering. Add onion and poblano and cook until softened and lightly browned, 3 to 5 minutes. Stir in garlic, chipotle, cumin, and mustard and cook until fragrant, about 30 seconds; remove from heat.
Stir processed potato mixture into onion-poblano mixture in a saucepan and bring to a brief simmer over medium heat to heat through. Transfer to a bowl and serve immediately.
Notes
Serve with corn chips or crudités. To rewarm cooled nacho dip, microwave, covered, in 30-second bursts, whisking at each interval and thinning with water as needed, or rewarm on the stovetop, whisking occasionally, and thinning with water as needed.